For fanfiction to be truly bad, it has to exhibit as many of the following qualities as possible:
1. Bad characterization. The characters must be completely out of character. This is not hard to find, obviously.
2. Bad *writing*. A lot of fanfiction is well-written, despite its other flaws. A truly bad fanfiction must be terribly written, complete with spelling and grammar errors.
3. Nonsensical, incoherent, or simply completely broken plot.
4. Some horrible perversion of the original characters that doesn't even make any sense.
A great work of (non-fan) fiction that satisfies most of these is the Eye of Argon. Everyone on 4chan should read it.