Continuity mistake: When Ramius is shot, he drops to the floor holding his wound with his left hand. He is still using his left hand when Ryan asks "What happens if he makes it to that ignition circuitry". The angle then changes, and Ramius is holding his wound with his right hand as he answers "He can incinerate the ship". New angle change, and Ramius is once again using his left hand on the wound. (01:56:35)
Continuity mistake: During the final battle, Borodin announces "Torpedo impact, 20 seconds". Ramius and Ryan discuss a book Ryan has written for the full 20 seconds, then Borodin updates, saying "10 seconds.." It's then a further 15 seconds before the torpedo actually hits. (01:58:10)
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)
Continuity mistake: The opening shots of Red October sub show water slapping against it. At the water line, the flat/vertical sides of the fake sub are visible - a very different look than the underwater model's tapered sides. (00:03:00 - 00:29:30)
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.
Continuity mistake: When Ryan is helo'ed to the Dallas it does not have a DSRV attached, but they use one later in the movie to board Red October.
Suggested correction: In the film more than 24 hours pass between the time Ryan gets on Dallas and when they show the DSRV attached to her. If you remember earlier in the movie it was stated that they could have the DSRV anywhere in the world in 24 hours. Therefore, one may assume that this time was used to get the DSRV to the Dallas.
Dallas was in the middle of tracking Red October and would have to have broken off the tracking (as it did anyway to pick up Ryan) in order for a sub tender to meet Dallas, place the DSRV on her, and then Dallas would have to hightail it back to find Red October. Plus getting the DSRV out to Dallas seems like a critical part of the story. While some scenes end up on the cutting room floor in every movie one has to wonder why there wasn't even a mention about having to surface for the DSRV.
Dallas didn't need to track the Red October anymore because the extraction point was already arranged, so it was very plausible the Dallas could get access to the DSRV.
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 Jack is getting off the plane in the beginning of the movie, his jacket collar is up. When he meets the 2 men who are there to pick him up, the collar is now down. (00:06:10)
Continuity mistake: When Sally is saying that Stanley is keeping her awake, her grip on the bear's ear is changing between constant shots. (00:04:40)
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.
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)