1. It is the 8580 which cannot generate the volume clicks. I know that because i upgraded my C64-II board with a 6581, re-enabling digi sound in all games. You can re-add this feature to the 8580 by tying the AUDIO IN pin to ground with a resistor.
It's a combination of the two on certain boards, more often than not with the later revision boards the leak is "fixed" and an 8580 on certain models of C128 will also play samples. It gets a little confusing to be honest, i was attempting to keep it fairly simple. =-)
2. You say features were removed from the 8580. Can you eleborate more on this? Because actually, except the new filter, the 8580 has a cleaner sound and more combined waveforms.
The combined waveforms aren't officially there (they're the sonic equivalent of pseudo opcodes =-) and some 6581 chips play them anyway but one of the pulse waveform settings doesn't work correctly on the 8580. The loss of a lot of the filter range is the biggie though, a lot of stuff just doesn't sound right and Martin Galway's most beautiful pieces sound really odd with the filters wide open.
Generally speaking, if you stick to the official guidelines for the SID anything you do will be cross compatible and it's only when the envelope gets pushed (excuse the terrible pun) that the differences become quite so glaring.