the amp, in my opinion, should do the following:
1) provide enough power to drive 4 to 8 ohm loads. in a reliable manner - most of them do that
2) provide enough power to handle low frequency transients ( like thumps, fast bass lines etc).
3) have a good design for handling high freq transients in an as close possible to a natural sounding manner.
4) have a really low floor noise with a good THD and signal to noise ratio (i understand anything over 70dbA is perfectly fine).
I believe that any deviation from ideality on these 3