The fact that, in writing one of his books, Clancy (who did not know how a United States submarine worked) managed to accurately describe it and its features. Among other things, the Americans in the novel are totally baffled by the Russian subs using a gravity-measuring navigation system - a system used in real life by American missile submarines, and existence of which was highly classified in 1984. He was then visited by the Navy, who had a few questions to ask.
What makes it even funnier is that he had extrapolated how it worked through simple library research. The Navy was in a panic over how this civilian had managed to obtain classified secrets, and these "secrets" were out there available for anyone smart enough to put all the pieces together, as long as they had a valid library card.
Ironically paralleled in the book itself. Skip Tyler manages to deduce, from the few scraps of information he's been given, that the Red October is trying to defect to the United States; the intelligence official whom he asks about this is immediately reminded of another man, back in the Vietnam era, who made a similarly accurate guess — from similarly disjointed bits and pieces of info — regarding a top-secret Army and Air Force raid on a POW camp.
Events like this gave security officers peptic ulcers.
Also hilarious is that when the FBI was sent to his house to question him, the conversation was (according to Clancy): "How did you obtain classified information?" "What information was classified?" "We can't tell you, it's classified."
When the US Navy locates the Red October, HQ marks it's location with a sub-shaped piece of wood with a Jolly Roger attached; The officer responsible had an odd sense of humor.
During the final shootout in the Red October's missile room, Alec Baldwin's perfect mimicry of Sean Connery saying "'Shome thingsh in here don't react too well to bulletsh.' Yeah, like me. I don't react well to bullets."
The comedic value of which compounds when after being fired on by The Mole, Ryan gives us the priceless line,
Ryan: I have to be careful what I shoot at?! (as the camera pans over to the nuclear missiles)
After steering the Red October into a collision course with a torpedo, while everyone is tensely awaiting their impending deaths, Ramius looks mildly confused by something. He turns to Ryan and asks, curiously, what books Ryan wrote.
Ramius then proceeds to troll them even further by saying they should be afraid of the Soviet fleet... until they leave, when he tells Borodin alone not to worry because he knows the entire fleet, having trained many Soviet commanders, and has an advantage. What Ramius really is concerned about is that he cannot choose the first American warship he'll encounter, and fears it will be manned by a "buckaroo" Captain who will shoot early and often the instant they make contact.
The revelation that Ryan speaks Russian when the Americans first board the Red October. Mancuso has decided that the whole boarding party should carry sidearms just in case, and has his own .45 prominently holstered on his hip, sparking a joke between Ramius and Borodin about the Americans being cowboys, a remark that Jack overheard and laughed at. Ryan explains to Mancuso that Ramius thinks he's some kind of cowboy.
The Oh, Crap! reaction from Tupolev's Executive Officer when he realizes that their own torpedo is about to hit them. "You arrogant ass! You've killed us!"
"Oh, Andrei... you lost another submarine?"
"You've dropped enough sonar buoys so that a man could walk from Greenland to Iceland to Scotland without getting his feet wet! So shall we dispense with the bull?"
The Flight Engineer of the C-2 Greyhound recalling a flight over the Sea of Japan where the turbulence caused even the pilot to throw up all over the cockpit and windshield, then elaborating on how it wasn't your typical puke, but 'huge industrial-sized chunks'. He's telling this to a green-looking Jack Ryan on an already horrifyingly turbulent flight while munching on a chocolate bar and offering it to Ryan.
Ryan: Next time, Jack, write a damn memo!
Doubling up with a Moment of Awesome, when the USS Dallas comes blasting out of the water while evading the Konovalov's torpedo. The Russian sailors aboard the American frigate don't know that the Dallas is in fact helping the Red October, and instead deduce that their badass captain had scared the Americans out of the water.
And after Ryan explains his defection theory (including biting the neck off a dissenter) it's capped off with Admiral Greer incredulously telling Ryan "I told you to speak your mind, Jack, but Jesus!" Great delivery by James Earl Jones. He's a combination of impressed, amused, and embarrassed.
The "Playmate of the Month" comment is sure to get chuckles, but then we cut to the bridge of the October and Captain Ramius' reaction: Jerk back and slam the periscope handles up, almost as if our dear Buckaroo Captain really was that rusty.
Actually, it's even better than that; Ryan comes up with a plan, totally made up on the fly, to get themselves aboard Red October, said plan requires Red October to go to a specific location. Mancuso looks at the message Ryan wants to send and asks, "Are you out of your damn mind?" At Ryan's urging, he sends it; cue Ramius' WTF?!? reaction.
Though one would doubt that any sailor would object to being sent a Playboy centerfold's measurements.
Combine the two and imagine what Ramius might've been thinking: "36DD...damn."
Alternately, think of it this way, Ramius has spent the entire movie worried that the first American ship he'll meet will blow him out of the water before he can say "I'm here to defect". Then, happening to meet a US sub that initially had its torpedoes pointed at him, he starts getting Morse saying "Oh, by the way, if you just happen to be trying to defect, we'll give you a hand". No wonder he's rendered speechless. After running for so long, trying to outwit everyone, someone just bluntly offers help before he's even revealed his intentions.
At the beginning of the scene in the Red October's officers' mess, Tim Curry, as Dr. Petrov, is relating some personal anecdote as detailed below. If one listens to the director's commentary, it's revealed that Curry ad-libbed that, and previously had been ad-libbing things to intentionallymake the other actors break character and crack up laughing, eventually reaching a point where they had to tell Curry to knock it off so they could get a usable take.
Dr. Petrov: Well, if you like borscht perhaps, but I've eaten better in an oiler's galley. My wife said to the waiter, "where did this man learn to cook? Afghanistan?!" So then we went on to the Bolshoi, the ballet, to see this new girl as Giselle. Well, you remember how beautiful she was! Well, she just married a factory manager and...
Sadly, we never get to hear the punchline because they had to send him away to give the officers privacy to discuss their plot.
As Tim Curry is known for his flamboyant and colorful characterizations, this is the only time in the movie where he gets to spice up the character (even if only a little), who is otherwise, as serious and subdued as everyone else.
The poor DSRV commander. In charge of a rescue vehicle, he really didn't sign up for this.
Steiner: Hey, I think someone just shot a torpedo at us!
Mancuso: No shit, buckwheat! Get the hell out of here!
Steiner: Well where am I— hatch slams shut
Jones using Layman's Terms to explain what a "biologic" is — a whale, then snarks it's something that knows sonar better than anyone else aboard.