How many holes will hanging a heavy panel on my wall require?
If you do opt to go with 1/8" ply, I'd suggest you use "washer head pocket screws" (1-1/4" if you have 1/2" drywall). If you're putting the sheets of ply sideways, I'd use a screw every foot or so on each stud. That might be slight overkill, but my thinking is to mimic the fastening of a sheet of normal drywall, which (a) needs to support the weight, and (b) doesn't flap loosely. 

Personally, I'd opt for a slightly more substantial ply (1/4") for better fastener holding. Whatever you use for mud, go for something that advertises "low shrinkage" on the label. Pre-mix is probably not a good choice; setting type compounds are apt to be better.