Deliberate mistake: In the scene where T& L are being pulled over for speeding, when they park, you see no protective rails on the side of the street they are on, but after they put the officer in the trunk and return to their car, on the passenger side, the rails are very visible.
Deliberate mistake: It's not particularly believable that the away team to stop the assassination would consist of the ship's entire senior staff, and raises the question of who was left in charge of the bridge (the answer: apparently nobody, as they return to a completely deserted bridge). Of course this is dramatic license, and at this point the audience won't care or likely even notice.
Deliberate mistake: Smoke from a smoke machine smells very acrid, is standard temperature and would never be confused with hot steam from a shower. The man with the knife would have suspected something is wrong once he was in range to smell and feel the "steam". (00:26:35)
Deliberate mistake: When everyone is surfing at night, the sound of the waves in the background is significant, as it should be. However, at one point, when Keanu and Lori are having an intimate conversation on the water, the sound of the waves disappear. The wave sounds resume in the next scene.
Deliberate mistake: The eyewitness testimony that placed Oswald in the lunchroom at the book despository didn't come to light until the House Select Committee on Assassination in 1978, many years after the Shaw trial.
Deliberate mistake: The number of acts Lecter performed during his escape from the individual jail cell and until he was attended to by an officer (who thought he was an injured officer) would have taken a lot of time and effort to complete - way more time than he could have gone undetected by one of the many officers in the building. Slashing/ bludgeoning to death a person can be done fairly quickly (munching on a victim's face adds time!), but three particular acts required a substantial amount of time, especially for an elderly man whose ultimate goal was escape: Swapping clothes (undressing and dressing) with a police officer and trimming off his face/scalp to appear to be that officer, then getting to a strategic location to be discovered; Setting a dead officer on the roof of the elevator; and, somehow hanging / impaling (crucifixion-style) an officer from the top of the jail cell (which appeared to be around 10' high). The latter feat would be challenging for TWO physically-fit officers.
Deliberate mistake: When Lithgow is shot in the leg and trips backwards over the crate or box, the stunt man is deliberately visible. It's not Lithgow making the fall.