In the scene in the interrogation room where FBI agent Stanley Goodspeed introduces himself to John Mason, John replies "But of course you are". This was exactly the same line he used when he met Plenty O'Toole in the casino scene in the Bond film Diamonds are Forever.
Arnold Schwarzenegger was offered the Mason role, but at the time the script was only 80 pages "with a lot of handwriting and scribbles and it didn't seem fully baked". In a Reddit AMA, he stated he regrets not taking the role. Years later, however, he still got to play a part as a convict with a mysterious past in Escape Plan (2013).
While the film was shooting, Alcatraz the island was still open to the public, and many visitors watched the movie being shot. However, on December 15, 1995, the federal government, which owns Alcatraz Island, partially shut it down due to stalled budget talks, and filming continued with no visitors present.
Don Simpson was largely responsible for creating the critical Gen. Hummel character. Simpson watched a 60 Minutes (1993) segment about the U.S. government's refusal to acknowledge soldiers who had died during covert overseas missions, and later read Col. David H. Hackworth's memoirs which harshly criticized U.S. planning during the Vietnam War. He combined these elements into Hummel's character and, as Jonathan Hensleigh described, created "a really compelling villain: a soldier with a noble end but, unfortunately, psychotic means."
At the beginning of the movie, General Hummel kisses his wife's grave stone and leaves behind his Medal of Honor, the highest award in the armed forces of the USA. It is bestowed on a member of the US armed forces who distinguishes himself "conspicuously by gallantry and intrepidity at the risk of his life above and beyond the call of duty while engaged in an action against an enemy of the United States"
Arnold Schwarzenegger was actually considered for Nicolas Cage's role in this film not Sean Connery's role. He also was considered for Nicolas Cage's role in Face/off which would have paired him with Sylvester Stallone, who was considered for John Travolta's role in that same film.
Each morning and evening the cast and crew made their way across the bay to location by way of the Red & White Fleet, a charter tour service, whose boats also carry the 4,000 tourists a day who visit Alcatraz.
The trivia items below may give away important plot points.
When Stanley and Carla are making love on the roof of their apartment, the Elton John song "Rocket Man" is playing in the background. This is the same song that Stanley refers to later in the movie when he kills Capt. Darrow.
Aside from the obvious references to Elton John's "Rocket Man", there is another, more subtle astronaut-themed reference: Maj. Baxter's first name is Tom, hence Major Tom, the ill-fated astronaut from David Bowie's "Space Oddity".