Generally I get more irritated by bland, sweetly-pretty renditions of familiar material than I do by outright incompetence; incompetent performances are often funny (cruel, I know) and they don't usually go on very long. As Bryan said, there aren't that many really incompetent singers who want to sing.

What I do find a bit trying is when a fairly high level of incompetence (say, for example, singing off-pitch, forgetting the tune, playing the wrong chords...) is combined with a blissful conviction of outstanding talent and a puppyish eagerness to share it with the room as often as possible. Someone like that can be a menace in a "jump-in-when-you're-ready" session - they're *always* ready. I think if I ever ran into someone like that, I'd be very tempted to retire to the back room and sing some songs in there with all the other refugees from the main room. Or something along those lines.