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."
During the final shootout in the Red October's missile room, Alec Baldwin's perfect mimicry of Sean Connery saying "'Some things in here don't react too well to bullets.' Yeah, like me."
The revelation that Ryan speaks Russian when the Americans first board the Red October. Mancuso has decided to strap a Hand Gun to his hip just-in-case, sparking a joke between Ramius and Borodin about the Americans being cowboys, a remark that Jack overheard and laughed at.
Ramius' calm explanation of why he ensured his superiors found out he was going to defect once he'd left;
(While calmly eating dinner) "When he reached the New World, Cortez burned his ships. As a result, his men were well motivated. Mm, this is good."
(Everyone else looks horrified).
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 Oh Crap reaction from Tupolev's XO when he realizes that their own torpedo is about to hit them. "You arrogant ass! You've killed us!"
"Andrei... you lost another submarine?"
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 Crowning 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 Bad Ass captain had scared the Americans out of the water.
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.
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.