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)
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)
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.