The rental car that Andrew drives is a 2004-2007 Ford Taurus. Cars are only kept by rental firms for up to a couple of years due to the wear and tear they tend to go through, so this car is far too old for a rental car (this film is set in 2014). A dashboard shot also shows a mileage of over 100,000 miles.
What Andrew is actually playing on the drums and what the audience hears rarely match up throughout the film. This is most noticeable in the final scene and is probably due to the fact that the drumming in so fast paced and intense that it would be nearly impossible to match.
When Andrew sits on the floor and is listening to a drum solo by Buddy Rich, the CD case indicated that he is listening to "Buddy Rich: Birdland". The solo that he is listening to is actually from the end of "Channel One Suite" which in on the "Buddy Rich: Mercy Mercy" album which was recorded from Caesar's Palace in Las Vegas in 1968.
At the JVC festival, a guitarist can be seen strumming to the tracks "Upswinging" and "Caravan", which does not contain any guitar work. However, in "Caravan", there is brief slide notes played on guitar after the brief trombone solo.
When Andrew is at the dinner table to tell his family he is the new core drummer and is interrupted, you can hear an audio overlay of him saying "core drummer" again. The camera is on him and he is not speaking so it appears to be an editing mistake.
During Andrew's first rehearsal, we see two quick close-ups of the pianist's hands. In the first, the piano has a descending line, and his hands also descend. The second is also a descending line, but we see his hands ascending instead.
During the retelling of the Charlie Parker/Jo Jones story, Fletcher says that Parker went back to practicing the very next day. According to Charlie Parker himself, he was so upset he didn't practice again for another three months.
In the first rehearsal of the junior band, the conductor is seen conducting a very fast tune in four-four. A concert band conductor might do this, but a jazz band conductor would conduct it in cut time.
Fletcher calls out Andrew for rushing on the 7th take, and dragging on the 8th take. According to one contributor to Reddit who used Ableton software to analyse the seemingly imperceptible differences in tempo, Andrew was actually drumming faster on the 8th take.
The alto saxophone players in the Shaffer studio band hold their instruments to their right side. Although this is standard for the tenor sax and other saxes that are larger than the alto sax, virtually all experienced also sax players hold the instrument directly in front of them (between their legs.)
When Fletcher drops in and asks the trumpets to play individually in the first rehearsal, the second player is supposed to make a mistake and does so, and sounds very bad. But anyone capable of playing in that band could never have sounded so bad; it was obviously an over-done mistake by someone who doesn't know anything about trumpet playing.
When Andrew and Fletcher meet for the first time while he is doing doubles Andrew looks up to see that Fletcher left and there is no jacket on the hook. When Fletcher walks back in and says, "Oops I forgot my jacket," the coat has reappeared on the hook.
During the final scene, when Andrew is walking towards his father, he drops his jacket. He is never shown picking it back up and when he makes the decision to go back on stage he drops his jacket again.
In the opening scene when Andrew is playing the drums there is a long tracking shot up the hallway towards the large doorway, however when Fletcher is shown standing at the door in the next shot one of the doors is closed.
In the final scene during Caravan, an absolute impossibility occurs. When Fletcher first attempts to end the tune, the band ends on a C#. Then Andrew goes off on his unscheduled 5 minute drum solo, which clearly was not rehearsed or planned. "Andrew, man what are you doing?"
Andrew indicates to Fletcher that he will cue him to bring the band back in for the final note.
However the now the final note is no longer C# but D...
How does the band know to play a D??
When Andrew is sitting with his father at the cinema as the lights dim, he is initially faced down looking at the ground, but in the next shot he is faced up looking at the screen, although there is no time gap suggested, as his father's conversation continues unbroken between the shots.
The file is set in NYC, however, when Andrew breaks up with Nicole, you can see the windows of the café are partially obscured by diagonal metal poles -- clear indicators of earthquake retrofitting, done in California to older buildings that are at risk of collapse in a quake. Buildings in NYC would never have had this addition.
When Fletcher kicks the trombone player out of the band for being out of tune, he congratulates the alternate and tells him that he is now on the fourth trombone part. But the piece they were playing (Whiplash) has only three trombone parts, plus a bass trombone. The player he kicked out was sitting on the end where the bass trombone would sit, but he was not playing a bass trombone. A top-notch college band would have a bass trombone player. And a jazz conductor would never refer to a bass trombone as a fourth trombone.
In the studio band, we see close-ups of the saxophones' mouthpieces and ligatures. These are clearly not professional mouthpieces and ligatures; top college jazz players would be using only professional equipment.
In Andrew's first rehearsal with the studio band, we see the trumpet players placing their cases on the chairs and opening them. The cases are made of cheap plastic and are made for beginner-level instruments. Top college players would never be playing such instruments and would instead be playing professional instruments.
When the Studio Band takes a break before Andrew (the "Squeaker") plays Whiplash for the first time he is shown in the hall writing notation on the Whiplash manuscript in pen. Presumably this is an original copy that he would not have had time to make his own copy/ copies for making notes- and an accomplished musician would not use pen for marking timings on music. Musicians only pencil so manuscripts can be cleaned (marks erased) and reused. Immediately in the next scene when Andrew stands and starts walking with Fletcher, Andrew is clearly carrying a pencil.
Twice in the movie there are shots of trumpets where the film was reversed so it appears that a trumpet is the reverse of how it is actually constructed. As an example, on a real trumpet, the lead pipe runs along the right side of the trumpet, and in the movie, there are two shots where the lead pipe is running along the left side. It appears that this was done so that the direction of the band - director being shown to the left with the horns blowing toward the left from the right - could be maintained.
The goof item below may give away important plot points.
(at around 17 mins) The first time Andrew attends practice, "Upswingin" can be seen among the scores as the other musicians are getting ready for the rehearsal. This is the piece that appears in the last scene as the new piece that Andrew supposedly knows nothing about.