I have not done owt too embarassing whilst singing, but in a theatre company in the late 80s on the Edinburgh fringe, I was playing the role of a downtrodden housewife and in my opening scene I had to stand and vacantly peel a carrot.

The peelings dropped on the shiny, well polished stage. Later in the same scene in a tense moment of threatened domestic violence when I was supposed to dodge a blow, I stepped on the peel and did indeed evade my abusive spouse by sliding in a skateboard stylee several feet across the stage. We managed not to laugh (just) but there was a wave of guffaws from the audience that rather destroyed the dramatic tension.