Factual error: Even though this film is set in 1965, Burlington Northern locomotives can be seen. The railroad was formed in 1970. Also, an EMD GP40-2 can be seen at the beginning of the film, but the first ones were built in 1972.
Factual error: Cochrane chases Murphy in a Hughes 500 which has a top speed of 147 mph and easily keeps up with him, demonstrating that Blue Thunder's top speed is less than 150 mph. The F-16s sent after Blue Thunder have a stall speed of 175 mph. They would have to slow down to the point of falling out of the sky to have a shot at Murphy. Its utterly impractical and far more likely that the military would have sent AH-1 Cobra attack helicopters after him.
Suggested correction: Not necessarily. The F16 (and other fast movers) can and do engage slow moving helos all the time. They just engage them by missile from a long distance, where speeds are irrelevant.
I'm no expert, but I wouldn't think the US Military keeps helicopter crews on Alert Status like they do for fighters. This film was during the Cold War, so maybe, but it wouldn't make sense to keep an attack helicopter crew (and ground crew) on Alert like they would for fighter jets. Even after 9/11, I wouldn't think a (armed) helicopter crew would be beneficial to keep.
Factual error: In the final gun battle at the end of the film, Harry shoots the last bad guy so he falls off a high spot on the roller coaster and through the roof, into the carousel building. Yet as the credits roll, there is an aerial shot and you can see the carousel building at the left of the screen, with no hole in the roof. Also, the carousel building and the roller coaster are about 200 yards apart.
Factual error: I don't know of any court system in the U.S. that will allow a person, teenager or not, to get into shootouts, steal a car, and maliciously run over/kill someone while fleeing a crime, and all they get is time in a juvenile detention center because they're underage. Whether you're a teen or not, if you commit crimes like that, you get tried as an adult, no exceptions, which means prison.
Factual error: One patient had a lobotomy. Impossible as those were abolished in the 1950's by the AMA and patients wouldn't be housed in the same room, too risky as they might attack each other.
Factual error: In one scene, our heroes go down a water slide with their bikes. Landing in the pool at the end would have made their walkie talkies unusable. But later they still work normally.