Capacitor considerations:

• DIELECTRIC COEFFICIENT   Briefly, since the capacitance per unit area is determined by the dielectric coefficient (usually expressed as K), this determines the size of the cap. Teflon, for example, has great properties, but its dielectric coefficient means that for a given capacitance, a Teflon cap will be larger (sometimes significantly larger) than some other types.

  A rule of thumb is that capacitors with high K dielectrics typically have worse temperature coefficients, but are smaller.

• ESR   Equivalent Series Resistance is the value of a resistor in the capacitor's model to account for its deviation from a perfect 90 degree phase shift. When doing analog circuit analysis, each component can be modeled by an equivalent circuit with mundane things like capacitance, resistance, and inductance, as well as exotic things like signal sources (noise generating mechanisms) internal voltage sources (rectification effects) and various frequency and voltage dependent parameters. The ESR is simply the resistance needed for the model to accurately reflect the real component's operation. There's also an inductive component I didn't mention, which can usually be ignored at less than radio frequencies. The capacitor's maximum Q in a filter circuit is inversely proportional to its ESR.
• Q   A derived value, the Q (quality factor) of a capacitor is a frequency-dependent value related to the ESR. Its value is equal to…
  Q = 1/(ESR*2πfC)

  …where f is the frequency in Hz and C is the capacitance in Farads. Since we know that a low value of ESR is good, it's obvious that a high Q value is also good. In choosing a capacitor, the Q should remain high and relatively constant over the frequency range of interest. Obviously, this condition will exist if the ESR is significantly lower than the capacitive reactance over the frequency range.

• DISSIPATION FACTOR   Another derived value, the dissipation factor is simply the reciprocal of the Q. Since a high Q value is good, a low value for DF is therefore good. In choosing a capacitor, the DF should remain low and relatively constant over the frequency range of interest. Obviously, this condition will exist if the ESR is significantly lower than the capacitive reactance over the frequency range.
• DIELECTRIC STRENGTH   Also known as breakdown voltage, the strength of the dielectric is expressed in the voltage required to pass through a specified unit thickness of the dielectric. There is an interaction between dielectric strength and K, with regard to size… The actual capacitance value is determined by both K and the thickness of the dielectric. The required thickness is, in turn, determined by the dielectric strength.
• DIELECTRIC ABSORPTION   DA is part of the capacitor model which represents the tendency of the dielectric to retain a charge. In this sense, the computer model features the primary capacitance in parallel with a smaller capacitance which itself is in series with a resistive component representing the dielectric absorption. In practical terms, low values of DA are desirable since they introduce hysteresis which can compromise the small signal transfer function.

  For audio, higher values of DA indicate potentially higher distortion at low signal levels. Another rule of thumb is that low K materials typically will have lower values of DA.

• TEMPERATURE COEFFICIENT   Defined as the change in capacitance per unit change in temperature. This likely has little audible difference with popular crossover caps. It is an issue with commercial (i.e. cheap) designs using non-polarized (NP) electrolytics. In addition to having low ESR and high DA/DF, electrolytics have quite high TC. With most popular film materials used in DIY crossover designs, the TC is low enough to maintain a stable value within the marked tolerance in the listening environment.
• INDUCTANCE   At audio frequencies, the inductance of a capacitor is usually not significant. However, if it does concern you, be aware that the smaller the capacitor (i.e. the higher the dielectric constant), the lower the inductance will be. Also stacked film capacitors have inherently much lower inductance than the more common wound film capacitors.
• MICROPHONICS   This shouldn't be an issue in a well-designed and constructed capacitor. Succinctly, microphonics are noise introduced by mechanical distortions of the component materials. Microphonics may be induced by external forces, or internal stresses.

• Picking Capacitors
• Learn Electronics - Capacitors
• Capacitor dielectric comparison chart

Following are my personal guidelines which others have found to be useful:

1. Film and foil is superior to metallized film, if you can tolerate the size. By superior, I mean primarily, lower noise. Capacitor noise is generally caused by flaws in the dielectric or poor terminations. The reason film and foil is "better" than metallized foil is one of metallized film's special "features". You will hear vendors speak of metallized foil as self-clearing. All this means is that if there's a pinhole in the film, a temporary arc will vaporize the metal around the pinhole. This is great for long term viability, but bad for noise since each time this happens, it adds noise. Also, most don't tell you that this only happens when the leakage current through the pinhole is adequate to heat the metallization to the point of vaporization. This is primarily a factor in polypropylene, since of all the popular high-stability dielectrics, it's the softest and therefore most likely to: a) have pinholes as received from the film vendor, and/or b) develop pinholes during winding. Finally, although the theory is that this only needs to happen once per pinhole, after which the metallization around the hole is blown away, it often doesn't work that way in practice. In the real world, all the metallization around the pinhole won't necessarily be cleared by the first (or second or third or…) peak.

   Another advantage to film and foil is lower ESR since the bulk resistance of the foil is lower than that of the film metallization. I expect this could play a role in any sort of capacitor-induced distortion, since as ESR decreases, the closer the cap approaches a perfect model. Whether the amounts of distortion potentially resulting from this would be audible or not is open to debate. Noise, on the other hand, is clearly measurable and therefore, presumably, audible as well.

   Finally, in any discussion of passive audio components, one consideration that can't be ignored is the dynamic range of the signals involved. This is why only better quality dielectrics are really suitable since their small signal and large signal characteristics track better than, e.g., NP electrolytics or even Mylar®. (This difference can also introduce measurable amounts of distortion.) This is also significant in noise… Since each pinhole may not be cleared by the first spike to come along, until it gets cleared, noise will be added to the signal. This becomes significant when you consider the 10-20 dB dynamic range of typical audio program material. In other words, those 100 Watt peaks may not come often enough to clear the pinholes since the average power is closer to 1 Watt. (This is also why non-inductive wirewound resistors are better in crossovers than film or bulk metal types, but more on this below.) This does, however, support the contention that metallized film may sound better after "burn-in". For film and foil, the potential advantages to burning them in become debatable.

2. Especially with polypropylene, the best caps used two layers of film. Doing so virtually guaranteed that the inevitable pin holes wouldn't line up. Single film and foil polypropylene is, unlike Teflon and polystyrene, only somewhat better than metallized film. Note: Most manufacturers consider whether or not they use two layers of film to be a trade secret, so you'll almost never see it advertised. However, it's often a safe bet that film and foil capacitors with excellent reputations are quite likely to be using them. At one time, AudioCap Theta's were noted as using two layers of film, but you won't find that factoid in any current official information. One notable exception is Intertechnik, whose Audyn-Cap Plus premium caps are advertised as "double wound".
3. Although significantly heavier, tin foil is generally preferable to aluminum foil, although the degree of improvement is debatable. Presumably, this is due to fact that tin is softer, resulting in less residual stress and reduced susceptibility to microphonics.
4. Stacked foil caps are generally better than wound caps since the material isn't stressed during assembly.
5. Impregnated paper caps (the paper is typically kraft paper and the impregnant is usually either oil or wax) can be quite good for audio, although for a number of non-technical reasons, they're less convenient and economical to use than plastic film types. Offering extremely low leakage/high resistance (but at the expense of high dissipation factor and often high inductance), they're still one of the best choices for high voltage work, but that hardly applies to audio. Of the choice of impregnants, wax offers significantly improved mechanical damping, but only at low temperatures - at higher temperatures, the wax melts and any advantage is lost.

   There are very few sources of impregnated paper caps for the simple reason that most manufacturers simply don't want to mess with them. Whether they offer audible improvements in crossover designs is a debate I really don't care to get into -  akin to the tube/valve vs. solid state or LP vs. CD debates. As with the tube/valve vs. solid state debate, there are measurable differences and no shortage of explanations on both sides why people might prefer one over the other.

6. Polyester (Mylar®) capacitors should be avoided for all critical applications! If your budget's tight, try using them in trap or Zobel circuits before putting them in the signal path. With poorer electrical characteristics across the board than polypropylene or polystyrene, Mylar® is the entry level for film capacitor dielectrics. For non-critical systems where cost is a major issue, they're at least better than NP electrolytics.
7. Polystyrene is a dielectric which is superior to just about all others. It's electrical properties improve on polypropylene and even Teflon®. Some premium crossover capacitor lines are made with polypropylene, but do they offer any audible improvements? As with many other issues, the improvement of polystyrene over polypropylene has been hotly debated. Many of polystyrene's electrical advantages (e.g. lower temperature coefficient) are irrelevant for crossover work where temperatures are relatively stable and drivers have looser tolerances which drift much more with temperature than crossover components. What's not arguable is that polystyrene has a much lower dielectric constant (K) than other dielectrics, so polystyrene capacitors are correspondingly larger for the same values.
8. Avoid oval caps! They're made by winding them round, then flattening them in a clamp while the epoxy sets. This leaves a lot of residual tension which can lead to value creep and microphonics.
9. Everyone buys their raw film from the same suppliers. Any vendor claiming to use, e.g., "premium" polypropylene film is, at best, exaggerating. Note that this applies generally to *virgin* film. You can also buy recycled PP film which is generally used for non-critical applications such as packaging and wrapping, or where only the mechanical properties are important. Although I don't know of any capacitor vendors who exclusively use recycled PP film for capacitors, it would be naive to assume that none do. Certainly, the type and class of capacitors I was discussing (MIL spec, low-noise, high reliability) all use virgin PP film.

   "Raw" polypropylene typically comes in pellets, either from a chemical company (usually virgin) or a recycler. Further clouding the issue, pelletized PP may contain a mixture of virgin and recycled material. The pellets are then fabricated into film by a mill, which may, or may not, be related to the raw material supplier. Finally, the mills are the folks who actually supply the film to the capacitor vendors. In the case of metallized films, yet another intermediate vendor is usually involved.

10. The biggest difference in vendors is QA of the winding operation (for wound vs. stacked foil caps, obviously). Constant light tension is required. This is especially critical with polypropylene since it has such little mechanical strength and stability (i.e. it stretches, tears, develops pinholes, and permanently deforms easily!)
11. The attachment of the metallization/foil to the leads is critical. This has to be a relatively low temperature operation or the film will be compromised. Poor attachment increases ESR and can introduce noise caused by rectification and/or thermoelectric effects.
12. If the rest of the structure is sound, the lead material is immaterial. Tinned OFHC is as good as you'll ever need.

13. Popular audio voodoo is that there's some magic in which lead is attached to which foil. These are all non-polarized parts! Since there are such wide tolerances in the component materials, capacitors are wound to a target value, then unwound as required to achieve the exact target value and tolerance. Until then, which foil is which is undefined.

Some well-regarded brands do sell exactly the sort of flooby dust that the preceding discussion attempts to debunk. As we all know by now, there's very little correlation between audio quality and marketing hype. I'd never rule out the possibility of a capacitor vendor marketing flooby dust, while still delivering top quality parts. The trap and the fallacy is in thinking that the parts' quality derives from the marketing claims, rather than simply sound engineering and manufacture.

DIY'ers spend ridiculous amounts of money for voodoo caps, when they could buy better caps, in most cases, from a wider variety of vendors if they only knew what to order. "Audiophile" caps are priced around the same as MIL spec caps, yet often have less to back up their claims of superiority.