My favorite fuck-up to have ever witnessed was while playing Spy in TF2. It was on Fastlane, and I was standing around disguised near the enemy team (Dead Ringer) waiting for them to start their assault on our point so I could chain-stab them. Suddenly I get kritzed, they rush, I chain-stab like half of them, then turn around and shoot the medic -- who is STILL kritzing me -- in the face. The best part is that afterward he asked in chat why the guy he kritzed started killing people, so apparently I just got lucky on a noob with a dropped Kritzkrieg.
For my own fuck-ups, I've gotten turned around a couple times as Engineer and set up a base on the wrong the side of the map -- usually from failing to notice that another Engy had their teleporter exit facing the wrong way.