Never seen flying squirrel 'round here (how do they taste?), but we do have the grays and reds... and chipmunks! I've never had problems with the grays, other than raiding bird feeders and maybe digging in the garden a bit. The reds on the other hand, get shot-on-sight... destructive pests. Up until this year I only saw the occasional chipmunk, but after we got rid of all our dogs last fall, the chipmunk population has exploded (and squirrels also). Brave little devils, they'll sit just feet away waiting for me to move so they can carry their stash into a building. So far, none in the house or vehicles, but every other building has become a home. I can see that without dogs around I'm gonna' haf'ta start shooting/trapping/poisoning all forms of rodent to keep the population in check.
As far as groundhogs/woodchucks... If'n I can see 'em from the house, yard or out building, they die. I've had the corner of a building collapse from groundhog tunneling in the past. Fool me once, shame on you... fool me twice, shame on me.
Mice, bats and the occasional rat? Sure, I live out in the sticks; I keep the mice and rats at bay with poison. Seems like we average one bat-in-the-house per year and it's always exciting, the girls scream and hide under blankets while the 4-year-old boy and I chase it around... knocking lamps and nick-knacks over, pictures off the walls, and whatnot.
Speaking of bats... back in the day, on hot summer days, we used to take a pontoon boat out on a wide spot of the river in late afternoon, loaded with beer coolers and shotguns. We'd sit working on emptying the coolers and wait for dusk... and then the fun would begin (dusk, or enough light to see, lasts for a long time on water). But, like everywhere else, civilization is encroaching and the yuppies movin' in out here got nervous about the midsummer gunfire on the river. One evening the sheriff came up river in the county rescue boat, he had a good laugh when he what we were doin... and then told us we'd haf'ta knock-it-off, as technically there ain't an open season on bats and we were frightening the "tourists" (as he called them at the time).
(Now that I think about it, all whoopin', hollerin' and such was probably just as unnerving to the "tourists" as the gunfire...LOL.)