Other mistake: In the final scene both at the start when Fletcher is walking on stage and in a shot during "Caravan," just after Andrew mouths FU, when Fletcher puts a hand under his jacket the shot goes forward and then immediately shows the same footage in reverse. (01:27:55 - 01:32:45)
Continuity mistake: In the beginning where Fletcher observes Andrew drumming for the first time, Fletcher hangs his jacket on a hook. A few seconds later after Andrew notices he's gone, there's no jacket hanging there. Shortly after that we hear the door open and it's reappeared. (00:03:20)
Continuity mistake: In the last scene, when the drummer starts the "caravan" song, the bass player on the left starts playing. But in the next shot he isn't.
Other mistake: Fletcher first says to play bar 93, then after 20 seconds of playing and many bars later, he says to play bar 115, but the music sounds entirely different. If the bars were correct, the band would have already played the music rather than a completely new idea. (00:19:45)
Audio problem: When they are playing "Whiplash" it shows a hand playing piano. When the hand is going up the piano (to the right) the music goes up, then down. Going up the piano should only play higher notes. (00:18:20)
Audio problem: When Nee-man gets his first blister when practicing the drums alone, he punches and breaks his fist through the snare drum. He continues to rock on with the snare drum audible in the practice exercise soundtrack, immediately after breaking it. (01:00:00)
Chosen answer: No, it is not normal to bleed while playing drums, as callouses develop on a drummer's hands through constant practising and playing. But, if a drummer plays hard enough and fast enough using the same drum sticks, friction between wood and skin can develop and rupture toughened skin. In the context of the film, the drummer is being pushed beyond his limits by the music conductor. Additionally, he is pushing himself to be better, so the bleeding is a consequence of that drive for excellence.