What they said. Plastic will ONLY keep birds in/out, it will do nothing whatsoever against dogs or racoons, not even the fairly heavy-looking plastic stuff.
As far as preventing digging, you *can* bury wire mesh but it needs to go down 18" if you wanna be really fairly *sure* that nothing will dig under, and that's a huge huge amount of work. Alternatively, and virtually-always better IMO because it is EVER so much easier and jsut about as effective, is to run a horizontal apron 2-3' wide of welded wire mesh. You lay it flat on the ground outside the run, SECURELY attach it to the base of the run fence, turn the outer edge down a little so it isn't conspicuous, and then either a) use a lot of landscape pins or tentpegs to secure it, or b) weight it down at strategic locations iwth big heavy rocks or concrete blocks, or c) dump mulch/gravel/stones/dirt/whatever over top of it, or d) peel back the sod before putting down apron, then replace sod over it [that's the hardest way].
Good luck, have fun,
Pat
