The first track to the Type O Negative album October Rust is titled "Bad Ground" which sounds relatively gothic and expected from a gothic rock band. The song itself is 30 seconds of just electrical noise caused by a badly grounded cable. I don't know if it's a mistake, but I always found it funny.

There is also Electric Light Orchestra's Don't Bring Me Down, where the mistake is that the lyrics "Don't bring me down, groos" was misheard so much as "Don't bring me down, Bruce" that they just started performing it with the misheard lyric.

Last but not least, there's Green Day's Good Riddance, where they start off keeping time, messing up and saying "fuck" before starting over and getting it right.