Is there a Campagnolo / Shimano compatibility issue for friction shift systems? I know that for indexed systems, mixing campy and shimano parts is a no-no. Does the same hold for friction drive trains?

The reason I ask is that I've never worked on campy parts before and I'm thinking of picking of an old Italian frame with a mix of campy and ofmega components with no wheels and I need to know what kind of wheels I will need.
In general, no.

Campy, Shimano, and Suntour (and other) friction shift systems are compatible because where the chain lands is up to you. 

There are some caveats that you'll have to resolve with trial and error. In particular some rear derailleurs have "longer reach" than others. You may not be able to shift to the largest cog on some freewheels if the derailleur is short (intended for racing). But that is not specific to friction systems.

You'll get the best results from friction mode systems if you stick with down-tube levers. Of course, these are compatible across vendors and some indexed levers even have a selectable "friction mode". 

Finally, it is posssible to mix campy and shimano indexed shifter/cogs if you use an adaptor. I use a j-tek and it works fine.