Factual error: An assistant to the Captain is wearing an Air Force uniform (as she should be). But it has no stripes on the sleeves. This would denote an Airman Basic. But no Airman Basic is going to be in an administrative position. (00:14:10)
Other mistake: Dr. Hynek and some Men in Black are aboard a boat. There is loud music playing. When Dr. Hynek tries to turn the radios off, power is cut off aboard the boat, leaving it in darkness. When they want to use the electric winch to raise something, the winch works. If there is no power, what allows the electric winch to operate? (00:26:15)