Excerpts from James Horner's score were taken directly from a piece of music from Aliens, and the Patriot Games, also scored by Horner. It is worth noting that both excerpts re-used by Horner are direct lifts from the Adagio of the Gayane Ballet Suite by Aram Khachaturian.
In the scene at the airport, where the President is answering questions about his friend (using Jack Ryan's advice to say that he and his friend were very close), you see a pack of media approaching the President. The lead newswoman, and the one who asks him the question, is actually Barbara Harrison, a prominent news anchor in Washington, D.C. on the local NBC affiliate station.
Several scenes were filmed in nearby cities of Mexico City: Cuernavaca and Tepoztlan. The scenes in Cuernavaca represent Colombia, when they are drinking coffee and the persecution following that scene. Also, Tepoztlan's Hotel Tepoztlan is where the drug lord lives.
The drug lord mansion destroyed by the missile was a real brick-and-mortar residence in Mexico purchased by the filmmakers from a divorcee who had unpleasant memories of the place. The filmmakers bought the mansion and destroyed it; the divorcee kept the land and presumably built a new house after clearing out the rubble.
The lines for the final confrontation between Ryan and President Bennett in the Oval Office were taken from an earlier version of the script after the filmmakers tried the intended version and found it lacked punch.
When discussing the final film, director Phillip Noyce admitted that he was disappointed in the climactic action sequence. He felt that it should have been bigger and more elaborate than the SUV ambush scenes in the middle of the film.
In the movie, CIA computer whiz Petey (Greg Germann) cracks the password of the boat victim by manually guessing combinations of birthday numbers of the victim's family. This is a relic of 1994, when the internet was fledgling and most people didn't have email or anything that required a password on their personal computers. By 2000, email and other online accounts had blossomed, and more people were aware that simple passwords weren't a good idea. In 2010 meanwhile, most websites have requirements on "password entropy" and reject outright such simple passwords as too easy to crack. On a side note, as a member of the CIA, Ritter probably had a "cryptocard" or other device that told him what his password was when he logged in, and changed every hour or every minute.
The trivia items below may give away important plot points.
In the book, Admiral Cutter is one of the villains for his support of the covert war, but Robert Ritter went from an ultimately-heroic character who supports Jack Ryan's effort to save the soldiers during the book to an all-out villain in the movie. In addition, the book ends with Jack Ryan condemning the President but electing not to expose the covert war (and a later Tom Clancy book reveals that the President deliberately lost the next election as penance for his actions), while the movie ends with Jack Ryan preparing to tell all about the covert actions in front of Congress. Screenwriter John Milius hated this story development because it made Congress look like a 100% noble body rather than a pit of snakes.
There are parallels between this plot with President Bennett and the real-life Watergate scandal with President Richard Nixon. Both hired agents to perform an illegal task (i.e. John Clark) and took steps to separate themselves from the agents. Both were caught using then-modern media: for Nixon it was hidden tape recordings in his office, and for Bennett it was a computer file. Once caught, both attempted to claim that the President's authority would overrule the investigation: Ritter's "get out of jail free card" is a letter signed by the President, and Nixon attempted not to release the incriminating tape recordings citing "executive privilege" (the Supreme Court later ruled this void). Both were investigated by Congress directly, and though Bennett's fate is unknown, Nixon resigned to avoid a certain impeachment and a likely conviction. The most poignant parallel between Bennett and Nixon is this: Bennett tells Adm. Cutter, "The gloves come off," while Nixon once said, "This is the time and this is the place to take off the gloves and sock it to 'em!"