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.
Answer: Fletcher recruited Neiman with the intention of ruining his career. He informed Neiman they would be playing songs he was familiar with, but secretly had other songs planned. Fletcher knew there would be influential people in the audience, whose opinion of Neiman would be made or destroyed based on his performance. Neiman attempted to play along with the unfamiliar songs, but couldn't. He decided to prove his talent by playing Caravan. This impressed Fletcher who was angry at first but came to respect Neiman and help him out.