[The module has] a number of reported bugs.
Ok, so it's broke.
[The module has] no unit tests.
This is the first problem I would address: Nobody touch nothin' until you figure out a way to test what you 'fix'.
Only after you can test any changes should you address the reported bugs. After resolving any code changes necessitated by these bugs, I would consider relapsing into "no broke, no fix" mode. Of course, if you're a programmer worth your salt, the list of 'problems' you have presented will greatly tempt your intervention. The issues most likely to draw my attention would be those bearing on maintainability. You must recognize, however, that you are venturing upon a slippery slope and may, willy-nilly, find yourself in full-on "can't fix just one" mode. Caveat programmor.