I've been having some small problems pop up on our board as of late, and I had a member suggest an "MP" of sorts to kind of police things, yet he suggested maybe it be someone anonymous. I know when a thread is closed or edited the admin/mod's handle shows up in the post, and on the "browsing" page it lists their title (admin, mod, etc.)...is there any way around this? Or even a better way to police the forums?

Not really - people know who the admins are. What might work is create a generic "Administrator" account and give the login to select people. They can be themselves but if they need to fix something, secretly login as the admin and make the adjustments.

Thus they can still be "one of the guys". I have a few people on a board who do that with a moderator login.