Goofs

At minute 16:50, the sub being shown underwater as the Tiger Shark is of a completely different profile and conning tower arrangement. The submerged sub having four antennas and the surfaced sub having only two.

The Tigershark appears to have pierced the saucer at a 30° angle, and the subs bow inside the saucer shows a 45° angle, yet all of the interior shots back inside the submarine are perfectly level.

At the end of the movie Holloway and Neilson walk outside during the day talking about the future. Neilson looks up at the sky and it is not a bright sunshine sky, but a night sky full of clearly visible stars.

The Magnetic North Pole is not located under the Geographic North Pole, which is where the UFO returns in the film to "recharge its batteries" from the Earth's magnetic field. It was first located in 1831; subsequent expeditions found that it shifts position over time.

While inspecting outside their submarine for damage the frogmen would not survive the arctic water in conventional scuba gear. The water in the Arctic Ocean is a steady 28°, and even at only 500 feet depth the water pressure on the divers would be over 200 pounds per square inch.

There is no Nobel Prize in oceanography.

Passengers are seen smoking inside the submarine while under the water. During this period smoking only allowed when the sub is surfaced.

At minute 30:50, stacks of dishes and cups are shown on an open shelf in the Officers Mess. Submarines, and also most surface vessels do not use open shelving due to rough seas and even typical steering maneuvers which would leave a pile of broken cups and plates on the deck.

Just as the saucer breaks through the ice, you can briefly see the rod with which the model is being pushed up.

At minute 44:20 when the Skipper tells Reef to make all engines full stop, the model being used in the underwater scenes has the propellers running in forward, rather than reverse as previously ordered, to extract the Tiger Shark from the saucer.

At the very beginning, the narrator is talking about the North Pole but there are snow covered mountains in the shot as the jets fly over. There are no mountains at the North Pole.

After the Tiger Shark rigs for "silent running," they continue to communicate over the loud speakers.

The alien saucer has enough advanced technology to make ships and submarines disappear in the Arctic Ocean, can deflect or freeze torpedoes fired at it, speak telepathically to humans, yet the cyclops has no defense against being shot in the eye with a pistol.