Other mistake: Murphy lands the helicopter on a railway line so an oncoming train will destroy it completely, and this happens exactly on cue with huge, dramatic explosions and flying debris. Apparently the train driver doesn't think this is important enough to interrupt his busy schedule - he doesn't stop the train. We do not hear brakes being applied - the wheels would make a noise like the sky coming down - and the train doesn't slow down at all - it just keeps on going.
Plot hole: Apart from the impressive pyrotechnics, what is the point of destroying the Blue Thunder helicopter? By far the most expensive, time consuming and technically complex part of producing any aircraft is the design and development phase - once the prototype is in the air production is relatively straightforward. The bad guys can make new Blue Thunders any time they like, and Murphy has destroyed the only evidence he has that there was a criminal conspiracy behind the whole programme - the 'videotape' he has of blurry, false coloured characters will convince nobody. Without the helicopter to back him up that tape is of no value to him.
Deliberate mistake: When Cochran sabotages the Jet Ranger helicopter by loosening the nut on the bolt securing the linear actuator governor, the bolt is inserted in the wrong direction. The bolt should have been heads up to prevent it from falling out as it did causing the helicopter to crash. Moreover, the linear actuator is on the opposite of the engine from where Cochran disconnected it. (00:38:05)
Revealing mistake: Right after a fleeing felon is shot dead and falls into the pool (whereupon Murphy says "He's bought it"), he appears to be swimming to stay afloat. (00:12:10)
Other mistake: The weather in L.A. sure is interesting, as well as the sunset/nightfall time. Near the end, before Frank Murphy notices the train and lands the helicopter, it is near sunset. The sky is still blue when we see a close-up of the train operator. By the time the latter notices the helicopter flying above the train, it is already night time. And just before landing on the rails, at night, the helicopter hovers a bit, and you can see that it is raining. When Frank exits the helicopter, it is a clear night. (01:43:00)
Continuity mistake: In the climactic chase scene, when Murphy is shot through the window, he is shot in his right arm and there is a hole in the window with blood on it. When he does a 360 degree loop in the helicopter the broken window and blood appears on his left sidethe opposite window to that which he was shot through. (01:42:20)
Revealing mistake: When the van gets flipped over outside the BBQ chicken place, you can see the cannon that flips the van over. (01:32:20)
Other mistake: Look carefully at the helicopter during the strafing scenes; at one point, the gunfire is not coming from the Blue Thunder at all, but from a Bell helicopter at a distance. Also, when we see the Blue Thunder helicopter during the attack, the cannon does not seem to be pointing at its targeted shots, let alone turning.
Continuity mistake: As the Chevrolet Vega arrives at the TV studio, the roof is shown to have sustained significant damage, as if something huge has fallen on it. The right headlamp area is also smashed and the light gone. But at no time in the chase does anything occur to cause any of this damage. (01:27:50)
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.
Character mistake: When Murphy shoots down an F-16, the guy says "we just lost a M-16."
Other mistake: His rank on the cap and the collars are different. Three rockers on the collars, two rockers on the cap.