Technology Marches On: The British police investigating the attack on the royals are quite impressed by Jack's "Cambridge Datamaster Model-C Field Computer", which has two megabytes of memory. Well, it is pretty impressive for 1983.
Backed by the Pentagon: The CIA scenes were filmed at the actual CIA headquarters; this was the first time the CIA had ever done such a thing.
Fake Irish: Only three actors in Patriot Games were actually Irish: Richard Harris, Patrick Bergin and Jonathan Ryan. This means all of the other Irish characters were this. Englishwoman Polly Walker plays the IRA terrorist Annette, though it is revealed in film that Annette is British-born (presumably of Irish ancestry).
Missing Trailer Scene: The line "There's never been a terrorist attack on American soil" was included in trailers for movie, but was left out of theatrical release because it sounded too much like an invitation or dare.
Old Shame: Alun Armstrong is said to be embarrassed by his involvement with the film.
The circumstances that led to Alec Baldwin not reprising his role for the film have been contentious and not fully-known until The New '10s. Baldwin claimed in a 2011 interview with Huffington Post that he was originally intended to return as the title character after starring in The Hunt for Red October. Instead, he was called by that film's director, John McTiernan, who informed him that the studio had gone behind his back and offered his part to an "unnamed actor" (likely Harrison Ford himself, who was previously intended to star in Red October before dropping out regarding concerns about the amount of screentime he'd have) who the studio owed debt to regarding a greenlit project the star was set to play in that fell through. Baldwin would then go on to accuse studio executive David Fitzpatrick of ultimately pushing him out of the role, under the pretense of giving him an ultimatum regarding filming dates. Baldwin ultimately decided to leave the project and star in a Broadway adaptation of A Streetcar Named Desire.
An unused climactic scene was filmed that would show Ryan and Miller fighting in the sea after they both fall off the boat, with Ford ultimately emerging victorious from under the waves and Miller drowning. Once test screenings were held, however, audiences criticized the scene for being too dark and looking like "two guys doing ballet". The final battle was changed to a boat chase instead.