Revealing mistake: When Crewe dumps the car in the river, you can see the wire attached to it that was used to pull it out of the water. Burt Reynolds mentions it on the DVD commentary.
Continuity mistake: After Burt Reynolds hits the guard in the crotch with the football, a wide shot shows 2:29 left in the game. He hits him again on the next play, and the scoreboard shows 2:35 left. The clock in a football game, of course, counts down, not up.
Continuity mistake: Suddenly, with no explanation, Samson is playing with his right arm in a cast and sling for the last two plays of the 1st half. Then he isn't wearing one in the locker room at halftime. He's on the sideline for all of the second half and is slinged up for most of the shots.
Continuity mistake: In the scene where Burt Reynolds is talking to the inmates before the first practice, hanging from a goalpost behind him is a tire goes from swinging slowly to swinging pretty hard during the entire scene. (00:47:10 - 00:48:50)
Continuity mistake: When Crewe and the other inmate are fighting in the swamp, the other inmate's shirt is pulled up, exposing his back. The shot changes when the other inmate points to a guard, and his shirt is now covering his back.
Continuity mistake: During one of the final huddles, Pop is standing right beside Crewe. The shot changes when the huddle breaks up, and Pop is not in the huddle anymore, and is standing 15 feet away beside the bench.
Other mistake: At the start when Crewe's girlfriend says "don't you take my Maserati" Crewe says he has earned it. He then goes out and gets in a Citroen, not a Maserati. Also, a Citroen front license plate appears on the car shortly afterwards which wasn't there before. (00:03:57)
Suggested correction: The Citroen SM model has a Maserati engine.
That doesn't make it a Maserati. Citroën bought Maserati in 1968, but their badge determined the brand, not what engine was in it. A lot of car companies are owned by other car companies to have multiple divisions in their lineup. If someone has a Toyota and called it a Lexus, they'd be wrong, just like it's wrong in this case.
Continuity mistake: During the game between the Mean Machine and the Guards, Nate Scarborough puts himself into the game. While he is in the huddle, Paul Crewe calls the next play, which is a "bootleg", and he says its "on TWO, on two". But when they go up to the line, he is calling the cadence and the center snaps the ball on ONE, not Two as it was called in the huddle.