I dont like Bugzilla and the other open-source bugtracking-systems. Thats why we did our own, and it isnt difficult to create. We integrated the user-rights (and user management) from our forum (in our case phpbb, but any other can be used as well) - so there is no need to create new account. I dont think most players would abuse it, have a look to the bioware-hosted forums, compare the number of users with the "abuse, spamm or flame"-content. I dont think that it is a big problem.
Same with the forums. But it would be better PR to show that you are interested in the bugs and their solutions. (I dont even think, that the use of a bugtracking system would cause 'bad' PR.)