Global 1025 is said to be a Boeing 757 and its cabin is a 757 cabin, but its cockpit is from a 747 and the black box simulation also illustrates the plane as a 747.
The dialog between Drake and the crew of Global 1025 is not the same once it is played by the Cockpit Voice Recorder (the "black box"). For instance, Drake's line: "Global 1025, descend immediately!" is skipped in the CVR playback.
On take-off, the order of the different speeds should be V1, VR ("rotate") and V2. The co-pilot says instead "V1, V2, Rotate".
The air traffic controller that shows the rookie how he works is violating procedures. He contacts three planes in a row with instructions without waiting for confirmation by these planes. Controllers always need confirmation that the aircraft has received and understood the instruction.
The facility manager of the Midwest controller station is part of the NTSB investigation team. As his station is subject of the investigation, he would never be allowed to be part of the investigation team.
A scene where Eric Stoltz is looking at aircraft wreckage, the reflection of the camera and a crewmember can be seen in the lens of his sunglasses.
Before the collision, Drake repeatedly calls the cargo plane on the radio and gets no response. Afterwards neither he nor anyone else mentions this.
In the movie, the NTSB personnel continuously use the expression "black box", even among themselves. This is unlikely for aviation professionals, who would call it a Cockpit voice recorder or a Flight data recorder (depending on which part of the black box it is).