Can a power cord increase the resolution of an Class D (SMPS) amp by more than 5% ?

Audioquest or no, its quite impossible for a wire in an AC power cord to express any directionality. To do so would be taking on characteristics of a diode as George (+1), kosst (+1) and Al (+1) have all pointed out.

What *is* possible  is that the shield of the cable might be hooked up at one end or the other (as opposed to the ground connection, which is the green wire) which *might* make a difference somehow, and certainly the finished power cord has connectors at either end that tend to make it directional :)

Put another way, its quite possible to hear differences in power cords and to also confirm the differences through simple measurement. OTOH, its quite impossible to hear differences in the direction of AC wiring, and this is easily confirmed by the fact that measurement of such yields a null.

When someone suggests to you that a wire in a power cord has a directional quality, the best plan of action is to turn in the other direction and run as hard as you can.

Since Geoff has discovered this thread, it will no longer suit to continue posting to it or reading it as per usual; snake oil has a highly ephemeral quality and much of it will be applied soon, yielding a similar result as with a directional AC wire.

Is there some kind of parameter or specification that indicates power cable bandwidth?

I've never seen one... it would be a good spec to include.

Looking at @dep14 's calculator, it looks like for a typical home-use power cord (16/3 cable at 6' in length) you're only losing .6% of your voltage on a typical 120v 15a home circuit,

In practice you see more- the problem area with many inexpensive cables in the connection at either end. That is where you are most likely to discover that the cable is heating up and this calculator does not take that into account. It also does not calculate the impedance of the cable at higher frequencies, so I can't regard it as 100% accurate, although for general home electrical stuff its fine.

The problem here is that, like it or not, you can hear differences between power cables. My thinking is that if you can hear differences, there should be something measurable as well. I find it easier to measure the effects on the equipment with which the cable is used rather than to measure the cable.

In a class D amp, the idle current is quite low. But to actually make the power to drive real speakers, the amp has to draw power from the wall and at full power can draw quite a lot depending on the amp. If you were to put an ammeter in series with the amp's AC power, you would see the meter dance around as you ran the volume up while playing music. The thing is, switching amps need the power supply to be quiet and the current it needs has to be readily available. Most of the expense of any class D amp is its power supply.

I’m having trouble seeing how a power cord could make a difference.  After all, the stock cable should be capable of delivering the full mains power available to the amp, and the power supply on the amp is going to clean up any minor amount of interference that could possibly sneak in between the wall and the unit.  

I've seen a power cord cause a loss of about 40 watts on a 140 watt amp. It was easy to see why- there was a voltage drop across the cord. I measured it with regular Digital VoltMeter (DVM); its not rocket science.

By contrast, the romex in the wall of most houses is much better performance, being made of solid core copper. But this material is illegal for use as a power cord; so yes, that last 6 feet can make a difference.

Here is an additional issue, that I think will affect switching amps more than other types of amps. The voltage drop is not limited to 60 hz. The problem is that there is a power supply in the amp that is made of a transformer, rectifier(s) and filter caps. The rectifier converts the AC from the transformer to DC and the filter caps store that voltage for use by the amp. In-between peaks of the AC power waveform, the caps get discharged. The rectifiers only conduct when the cap voltage is lower than that of the transformer; if the caps are only slightly discharged (the normal state of affairs) then the time that the rectifiers turn on is very slight, perhaps a few milliseconds or even microseconds. At that time the current draw might be profound; if the power cord does not have the bandwidth, the pulses charging the caps will be current limited.

This can be bad for a switching amp, which needs a really clean power supply to sound right, even if they don't seem to be drawing much power from it at any given time. So its worth it to try a power cord that has greater bandwidth (which romex already has...).