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: When we see the door to Elisabeth's, her name is spelled with a s. Later when Nick looks her up on the computer, it's spelled Elizabeth.
Character mistake: Leland Palmer handles Laura's body without any gloves when wrapping her and disposing of the body. As with any respectable FBI investigation, upon finding her body and checking for fingerprints, they should've connected Leland to Laura's death within days. (02:05:00)