The agents believe the failed airplane bomb was set to go off at 20,000 feet. This is not true, it was a timer which partially failed. Cargo holds are pressurized (the whole interior is), altimeters of that time work on air pressure and so would not work.
The movie claims that the field of Forensic Linguistics had not been invented/discovered prior to Fitzgerald's work on the case and that he invented the term. The term actually goes back to 1968 and many cases in the UK and Australia had been solved through analysis of discourse and writings of suspects prior to 1995.
When they're on the phone to clear flights from LAX there is a KLM pilot that says: KLM206. That is a wrong flight number for a flight from LAX to AMS. The right flight number is 602.
The only FBI agent that ever interviewed Ted Kaczynski in person was agent Max Noel (now retired). Agent Fitzgerald never met Kaczynski. The only other law enforcement agent to met and interview Ted Kaczynski was Postal Inspector Paul Wilhelmus.
This was a 'creative license' taken by the creators of the show, only for dramatic reasons. So the entire scene is fiction.