Certainly you can imagine many ways to get rejected by a co-op board, but hopefully these aren't things you'd actually do -- talk about the kickin' bachelor pad you've always wanted or arrive to a morning interview with whiskey on your breath. That said, there are many sneakier pitfalls that can hurt your chances of being accepted to the co-op.
That's mostly because co-op boards have the legal right to be rather arbitrary. The 1990 Court of Appeals decision in Levandusky v. One Fifth Ave. Apt. Corp. allows co-op boards to use "business judgment" when accepting or denying applicants [source: Kaye]. As long as decisions aren't discriminatory, the board can deny you for any and every reason it sees fit -- in New York City and most other places -- without having to explain the basis for this judgment.
Buying into a co-op is less like buying real estate than like joining a club. Instead of you owning the walls and doors of your apartment, they're owned by the club, whose share prices fluctuate in direct response to your occupancy. By living in this building, would you contribute to the club atmosphere and bring prosperity and goodness to all, or would you drill holes in the hull of the collective ship, sinking the building to the bottom of the deep blue sea? It's the co-op board's job to decide.
The following are common things that turn the tide of "business judgment" against co-op applicants.