Aside from one instance of terrible frame rate dropping to single figures during a side mission, with you in a spaceship, the only other bug I've had in my time playing the 360 version was a repeatable bug caused by having Keith David audio log 3 playing, as it tried to start the audio for the next quest, as The Touch was playing on my MixTape, which resulted in the jump I was doing causing my The Boss to go flying some 10,000m away from Steelport, which was actually kinda funny to watch, and easily fixed by not trying to jump.

I had an object that I needed to use telekinesis on fall through the world geometry, making me restart the mission. Also, this happened.