Character mistake: Characters refer to the Dallas and the Red October as "ships," but anyone stationed aboard a submarine would know to call it a "boat."
Factual error: When the USS Dallas submerges to attack the Red October, they rig for battle stations as well as rig for red. On a submarine, rig for red is only for periscope depth operations at night, to allow control room watchstanders eyes to adjust to the darkness topside. No other area on the boat rigs for red. Throughout the movie the lights darken along with battle stations. No naval ship would reduce visibility on purpose in a heightened state. (01:31:00)
Factual error: When Jack Ryan is chasing the Cook's Assistant Igor Loginov through the missile compartment, the compartment shown does not exist. Russian Typhoon submarines (of which the Red October is a variant, just with a new propulsion system) have a pair of cylindrical pressure hulls - each containing a missile compartment - on either side of the missile tubes. The location where the fight takes place in the movie would be inside a free-flood area in a real Typhoon. (02:01:20 - 02:05:00)
Visible crew/equipment: When the Red October sub has surfaced to let the crew get off because of the supposed nuclear leak, there is a brief shot where you can clearly see the camera and its filming crew in their tennis shoes on the deck. (01:45:52)
Factual error: Aboard the aircraft carrier, there is a closed-circuit TV that shows the operations on the flight deck. At one point, a gull-gray F-14 Tomcat, in obvious distress, comes in for a landing. The camera cuts away from the TV to Ryan's face, and the cuts back to the TV. All of a sudden, the plane crashing is no longer an F-14, but an old Korean War-era fighter (F-9F Panther of VF-21), colored the dark blue the Navy stopped using in the 1950s. The director chose to insert a piece of stock footage from George Duncan's crash on the deck of USS Midway (CV-41) on July 23rd, 1951 rather than build a model F-14 to crash for an otherwise unimportant scene.
Factual error: In the opening scene of the movie, the Red October is being escorted out of the Russian harbour by a United States Coast Guard Cutter and U.S. Navy sea tugs. (00:02:30)
Suggested correction: You may be aware of the fact that they used American boats (I doubt they had access to Soviet ones), but there are no distinctive American markings or livery visible. Most notably, you don't see USCG racing stripe in the boat to starboard (the only one which is not a tug).
Factual error: At the beginning of the film Jack says goodnight to his daughter and then leaves for the airport to catch the flight to Washington. He arrives at Heathrow in the dark. A flight to Washington From Heathrow takes 6-7 hours, and Washington is 5 hours BEHIND London. If Jack leaves at, lets say, 10PM London time, he would arrive at midnight US time. But in the film he's met upon arrival and gets straight into a car at the airport and drives to the CIA offices for his meeting with Greer. The problem is it's daylight when we see the car driving to Langley, which is a relatively short drive from Washington and the Airport (s) - where did the night go? (00:06:00)
Revealing mistake: In the scene where Jack Ryan is brought aboard the U.S.S. Dallas after releasing himself from the helicopter, two crewmen drag him inside. The crewman on the left side of the passage backs into a metal valve, but the valve moves down and left, then snaps back in place as if mounted to a rubber pipe.
Factual error: The Hunt for Red October takes place sometime in late 1984. The Oliver Hazard Perry Class Frigate Reuben James (FFG-57) on which Adm. Greer and Skip Tyler were on board in the latter half of the film, was not commissioned until March 22, 1986.
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)
Visible crew/equipment: When Jones the Sonar operator detects the Red October for the final time via his headphones, he is talking to someone next to him. The whole time he is doing this, a microphone boom is constantly bobbing into view from above his head.
Revealing mistake: None of the exterior storm scenes where rain is present have any visible impact on the actors. No water or mist on face, binoculars, hat brims, etc. The special effect that creates the rain does not correlate to the either actor appearance or background reality - sun reflections, clouds, etc.
Other mistake: When the Political Officer reads the orders, they're supposed to test the silent drive and return home "on or about the 16th of this month." Shortly afterwards, Jack Ryan is briefing Jeffrey Pelt, and asks "isn't it the 23rd?", meaning the 16th of the month is in the past.
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)
Visible crew/equipment: In the scene where Ryan is being flown out to the Dallas, the door crew member looks out and says, "Yo, got a sub about 2 miles out." If you look closely in his goggles, you can see the reflection of the crew. (01:45:30)
Deliberate mistake: Morse code takes a lot longer to type out than the captain of the Dallas seems to need. Likely "compressed" because otherwise the process would be quite dull, but still.
Factual error: When Ryan is brought on board the Dallas, Captain Mancuso climbs down from the conning tower, through the hatch next to the control room of the sub. He then walks/runs down two flights of stairs and enters a short corridor where Ryan is now dropped on the floor by the safety diver and another crewman. I am unsure of the exact location of the lower hatch of the escape trunk on a 688 sub, but I suspect it would be on mid deck. When the camera turns to face Mancuso again you see the curvature of the hull next to him, suggesting this takes place on an upper floor on the sub. So why did he run down two stairs to seconds later end up on the top floor of a sub with only three floors inside the pressure hull?
Suggested correction: All escape trunks on all submarines are on the top of the pressure hull. The lower hatch would be a few feet below the top of the pressure hull. The only deck (floor) to be able to reach the escape trunk is the upper level (top floor), so the shot must show the curvature of the hull. If it didn't, then it would be a factual error.
On 688 class submarines such as the USS Dallas, the forward escape trunk lower hatch is immediately aft of Crew's Mess in Forward Compartment Middle Level.
Factual error: In some stateroom scenes in the October the bulkheads have numerous little lockers installed because storage space on a submarine is at a premium. The latches on the lockers are of a unique design created only by USA Navy ship and submarine construction shipyards.
Suggested correction: Given the vast step upwards in technology and the power of Soviet Intelligence at the time, there's no reason why they shouldn't know about something as least classified a latch on a locker.
Suggested correction: The Soviets stole from the US like it was a bodily function, to the point where, in anticipation of such, our engineers would put microengravings mocking them "when are you going to stop stealing" in Cyrillic, on the surface of computer chips et al. The only real objection to the presence of those lockers is that the Soviets would have bigger fish to fry in terms of copying.
Revealing mistake: Near the end of the movie when the Russian attack sub gets hit with the errant torpedo, the shot from the "Ruben James" shows the explosion from the surface. In the middle of the large wave generated is the puff of black smoke and a pyrotechnic flash which triggered the explosion.
Deliberate mistake: The torpedo hitting the water dropped by the Russian Bear Foxtrot, and the one dropped by the Americans are the same piece of footage.
