The media lab has done a ton of research on this. I seem to remember people being able to notice visual latency at 30ms and audio latency at 80-120ms (this is because light is faster than sound).
Any rhythm game player will disagree.
Some games (e.g. llsif, for android) have "perfect" window sized to 16ms (a video frame). Even with latency compensation, these are unplayable on bluetooth yet fine on headphone jack. As the game has calibration, the resulting offset is seen to be at least 30ms worse on bluetooth.