On two occasions flights of English Electric Lightning fighter jets are seen under the command of a US battle group. Lightnings were never flown by the USAF, but only the British RAF and a couple of small nations. Of course, seeing this happens in the future, anything is possible.
Strings guiding the shuttle from the saucer can be seen.
Assuming that a submarine's control room plotting table would be bolted to the floor, the plotting table moves when Captain Crane falls against it.
The sound heard from the helicopter at 5 minutes in is the wrong sound for this type of craft. What is heard belongs to a Bell 47G-2 or similar as the sound of a tail rotor and 2 bladed main rotor is heard. The Boeing Vertol CH-46 has two 3-bladed main rotors.