Character mistake: Lt. Caffey (Tom Cruise) wants the two marines to plead guilty and take a deal because he doesn't want the to "spend the rest of their lives in Leavenworth (prison)." The United States Disciplinary Barracks is indeed located in Leavenworth, Kansas. And the US Army and US Air Force send convicted felons there to do their time. However, Marines and members of the United States Navy are sent to Portsmouth Naval Prison in New Hampshire. It is run by the Marines.
Suggested correction: It's perfectly within character that Caffey wouldn't know this. He's been in the navy a short time, never tried a case in a courtroom, and is generally uninterested in military protocol.
Character mistake: The "MAC-10" machine pistol used by Darryl and Sergeant Murtough is actually a Cobray M11/9.
Character mistake: During the end credits, three of the magazine covers spell Whoopi's character's name as "Delores." Two of the covers spell it "Deloris," as do the credits.
Character mistake: When Cutter is talking with Chief Biggs for the first time, right after the negotiations for fuel, Cutter says he is the former head of security for the airline. Since he has just been hired for that role (after being an independent security consultant), he should have called himself the future head of security, or new, or something of that nature. Former would indicate he has resigned from the position.
Character mistake: Lisa is testifying about the 1963 Pontiac Tempest and the 1964 Buick Skylark being the same height, width, and wheelbase. While the Tempest and Skylark shared the same components, the 1963 and 1964 models were quite different from each other. The 1964 Skylark and Tempest moved to a 115 inch wheelbase and a larger body and frame. The 1963 Skylark and Tempest were smaller with a 112 inch wheelbase. An expert as she claims to be wouldn't confuse the two.
Character mistake: Bruce Wayne talking to Selina Kyle says that Batman probably saved millions of dollars in property damage alone. When Batman first saw Catwoman he didn't do anything to prevent the property damage before the explosion that she caused.
Character mistake: When Greer and Cantor visit Ryan's home after Miller's escape, they state that he was being moved to HMP Albany on the Isle of Wight (correct, given it was a Cat A dispersal prison at the time and regularly used for IRA prisoners) however Greer later states "it happened in Kent, near the channel", which is incorrect. Lymington (as stated by the guards over the radio in the escape scene) is in southern Hampshire - over 90 miles away from Kent and on the other side of the country.