When Dr. Ames and the crew member are fighting in the missile room, his diving mask gets knocked off, the last time he gets hit. Then a split second later in the next shot, he has it back on.
As the Seaview is damaged and unable to take on the monster jellyfish that has trapped Ames, the scientist, the flying sub is launched to distract the monster.The launching shows two shots of the flying sub leaving the Seaview,not at a submerged depth,but on the ocean's surface.There was no time for the Seaview to make such maneuvers to the surface.
At one point, Ames tries to hold the ship hostage to his will by hot-wiring a torpedo through a very noticeable, bright red inspection hatch on the side of the topmost torpedo. Prior to that shot, that torpedo - and all the other torpedoes lining the racks - are all black-and show no bright red inspection hatches.
About 39 minutes, the laboratory "power" meter is actually an automotive dwell tachometer used for adjusting ignition points on cars without electronic ignition. The words "4 cyl, 6 cyl and 8 cyl" were visible which refer to a car's number of engine cylinders.
After the admiral orders Kowalski to "handle the parabolic mirror" to free Captain Crane in the flying sub,the camera pushes in to follow Kowalski,and the shadow of the camera can be seen on the bank of instruments on his left.