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)
Chosen answer: He was fired from the university, but the band at the end was a hobby group he had started conducting for.