Here are some highlights:
Staples. Exposed staples in the center binding are a rare but serious hazard. As a last resort, pianists will press down the center fold to make a book stay open. Each one of us has ended up bleeding on the keyboard after a run-in with center staples.
Pages in backwards. Or upside down. Or not there at all. You laugh. It happens.
The last one happens more than you might think. Once in an audition when I noticed a page missing on an unfamiliar aria, I stopped playing and drolly said "Um. You're missing a page." to the horror of the singer and amusement of the panel.
Another potential problem occurs when singers do not or cannot lead a tempo when singing. An audition is one situation where the singer must take the initiative tempo-wise, rather than hoping that the pianist will push them along. The singer who sings behind the beat in an audition creates a double-whammy: the pianist can either 1) push them ahead and risk leaving them in the dust, or 2) follow their tempo and watch them fall flat. Neither option bodes well for the singer.
On a serious note, one of the single most important intangibles a singer can get to work for them is presenting properly organized and marked music to their pianist at the audition. That sends a signal to the pianist that they are playing for a professional and someone to be taken seriously as a potential degree candidate (at the university level) or potential colleague (at the professional level). This first impression goes a very long way, not to mention minimizing risk in the high-stakes one-shot game of auditions.