Cowboy Bebop at His Computer: Part of the St. Petersburg tank chase was filmed on site. They faked all of the relevant statutes and treasures and smashed replicas on a UK Backlot, but that didn't stop a few breathless "They're destroying our art!" newscasts in Russia.
The unfortunate Admiral who suffers Xenia's thighs early in the film previously appeared in the "unofficial Bond" Never Say Never Again. Presumbly his murder was punishment for starring in the Thunderball knockoff.
Method Acting: Before filming the sequence in the sauna where Bond hurls her into the walls, Famke Janssen encouraged Pierce Brosnan to run her into the wall as hard as he could, and actually insisted he do it, citing that the walls were padded; Cue irony as Famke promptly managed to break a rib after Brosnan did as she demanded, the very damage her murderous thighs are meant to do in-movie.
Star-Making Role: Partial Aversion. Pierce Brosnan was already famous when GoldenEye was made, but after Remington Steele (which put him on the map) he lapsed into mediocrity. Bond revitalised his career greatly, to the point that he's the only Bond other than Sean Connery to have an active and lucrative film career.
Technology Marches On: The movie came out in 1995. Natalya goes to an IBM office so she can contact Boris via the internet, and gives the sales rep a purchase order as a rather clever lie to use their connection. Computers using 500 megabyte hard drives, with 14.4 kbps modems, seem woefully underpowered today.
Alan Rickman turned down the role of Alec Trevalyen. There was also talk of Anthony Hopkins playing role, with Trevelayan originally intended as having been a mentor/father figure to Bond rather than an equal.
A subversion from a previous example. Pierce Brosnan was originally chosen to replace Roger Moore as James Bond but wasn't able to get out of his Remington Steele contract leading to Timothy Dalton getting the part.