Revealing mistake: In the scene where Ryan is chasing the undercover KGB agent through the missile compartment one of the valves on the missile tubes is very wobbly as it is bumped. Although given the state of the Soviet Submarine Force maybe this is accurate....
Continuity mistake: As the helicopter nears the Dallas sub, Ryan is in the right-side doorway at the rear of the opening. A spotter is on the same side of the craft, at the front of the opening. The spotter looks straight out the right side of the chopper and shouts for the pilots to turn left, as he has spotted the Dallas at three o'clock (which is where he is looking). But turning left moves away from the Dallas, not towards it. (01:23:30)
Other mistake: Even though Ryan was warned earlier that the water was so cold that you could survive in it for only four minutes, he doesn't even shiver while drinking coffee in his wet clothes inside the Dallas. This after plunging deep underwater from his fall from the helicopter and then waiting to be rescued and brought aboard by the diver.
Revealing mistake: In the scene where they are dropping Ryan from the helicopter to the submarine, you can see that they used the same actor for both the pilot and the co-pilot of the helicopter. You can see the mirror image on the helmet of the pilot in one of the shots. It appears they just changed the voice actor only.
Continuity mistake: When Jack Ryan is being flown, via chopper, to meet up with the USS Dallas, the pilot expresses concern for the fuel situation. First we see this pilot in the right-side seat from a good distance behind his left side as he is talking. When he looks back at Ryan in close-up, the shot is backwards so that he seems to now be in the left seat, looking over his right shoulder (notice his name on the helmet is backwards). Then, after the sub is spotted, he speaks again, and is seen back on the right side, looking over his left shoulder at the left-side co-pilot.
Factual error: Regardless of the factual error about the visible distance in Atlantic waters, just before the Red October and the Dallas communicate via Morse code, there is a scene where both submarines are diving upwards. The two submarines are hardly more than 50 yards apart even though, only a few seconds earlier, a crew member said that they were about 300 yards apart.
Continuity mistake: When the aircraft crashes on the carrier, the Admiral, Captain and Ryan are in the island (the superstructure on the starboard side). In the next shot, they are looking at the crash from the port side. You can see the island, where they were moments before, in the background.
Continuity mistake: At the end of the movie in the scenes with Connery and Baldwin on the tower of the sub, the light of the moon is obviously shining on their faces but the reflection of the moon stretches out across the water behind them.
Continuity mistake: When chasing the KGB agent, Ryan climbs up a ladder empty handed, but when he rolls over on the walkway he has a gun in his hand.
Other mistake: When the sub is ordered to turn right, Ramius is seated facing forward and tightens his seat belt. When the sub makes a tight right turn, his coffee cup slides the wrong way. (01:00:01)
Revealing mistake: Near the end, when Ryan and Ramius are talking, right before Ryan says "welcome to the New World", Ryan is facing Ramius and his thick hair should be blocking the hill in the distance behind him, but his hair is translucent and the hill is visible through his hair. (02:06:00)
Continuity mistake: Towards the beginning of the film, when Captain Marko Ramius kills Political Officer Putin, Ramius initially grabs Putin's face and forehead from behind, pulling the political officer off balance and into the edge of the table at which they were just sitting and discussing their orders. In the cut just before Putin slumps to the floor and falls backwards, Ramius' hand is now high on his victim's chest, near the collarbone.giving an extra push. Putin also moves some distance towards the door as he falls backwards onto the deck and dies. (00:18:30 - 00:19:00)
Character mistake: As the helicopter crewman sees the Dallas surfacing, he says something along the lines of, "Sub at three o'clock". The next shot is from inside the helicopter and shows the sub and a part of the starboard landing gear retracting pod. This shot puts the Dallas closer to one o'clock. (01:24:00)