Hmmm... Let's see... One time, I was recording a screaming vox track for a metal song I was working on, and my cat ran up to me and started meowing like crazy. I stopped recording to pay attention to a very worried cat.
And there was another time I was recording for a competition project involving vocals (an atmospheric peice that could only consist of the phrase "There was a hole here, it's gone now,"), and I got an Xfire message during the recording session and didn't notice my mic picked it up until I had added delay and mixed it with the main vocal track in Audacity. I was too lazy to record that huge chunk again, so I left the beep in there.
Other than that, not too many problems.