There were tensions during shooting between director Michael Bay and Walt Disney Studios executives who were supervising the production. On the commentary track for the Criterion Collection DVD, Bay recalls a time when he was preparing to leave the set for a meeting with the executives and was approached by Sir Sean Connery in golfing attire. Connery, who also produced this movie, asked Bay where he was going, and when Bay explained that he had a meeting with the executives, Connery asked if he could accompany him. Bay complied, and when Bay arrived in the conference room, the executives' jaws dropped when they saw Connery appear behind him. According to Bay, Connery then stood up for him, and insisted that he was doing a good job and should be left alone.
Sean Connery was rumored to have asked the production to build him a cabin on Alcatraz so that he wouldn't have to travel to the mainland every day. In reality, Connery allegedly did ask permission to anchor a yacht off the dock of Alcatraz but was denied by the Coast Guard. No cabin was built but he would spend time in his trailer whenever he didn't want to go back to the Hyatt hotel in San Francisco where he was staying for the duration of the shoot.
According to director Michael Bay, the script was written much more straight and serious than the final movie. Most of the humorous moments and lines were improvised during filming.
The premiere of the movie was held in the Prison Recreation Yard on Alcatraz.
While filming, Alcatraz 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, partially shut it down, due to stalled budget talks, and filming continued with no visitors present.