Continuity mistake: When Joe and Milo are up on the steel structure where the stadium lights are, just before Joe throws the bag of ammo over the edge, a sniper runs to the right in the background, then in a following shot, the sniper runs to the right again. It is the same sniper. (01:31:15)
Continuity mistake: When Jimmy Dix is in the bar, and says " to Alex the astronaut" he is holding the glass with his left hand. In the following shot he drinks it with his right, then it switches back to his left. (00:19:10)
Continuity mistake: After Joe kills Chet by punching his nose up into his brain there is an instant cut and as Chet is collapsing to his knees, he already impossibly has a stream of blood running out of his ears all the way down to under his shirt collar.
Continuity mistake: Big Ray Walston screams that his nose was broken, and has blood coming out of it, despite the fact that Jimmy Dix blatantly hit him in the forehead with a football. (00:12:00 - 01:25:10)
Continuity mistake: Near the beginning of the film where we see Joe and his best friend Mike standing outside of Joe's house, if you look Joe is standing in front of the tree and his car is parked in line with the tree, yet when Mike walks away and Joe turns around, the car is now parked almost in front of the tree, and Joe is standing behind the tree. (00:16:35)
Continuity mistake: When Joe has been kidnapped, and then killed one of the bad guys, Milo says to Pablo, "Take the corpse out of here and fix Mr Hallenbeck a drink." Pablo is holding his gun in his right hand, but in the next wide shot Pablo is now holding his gun in his left hand. (01:03:10)
Continuity mistake: When Joe and Jimmy are walking down a tunnel going to Marcone's office, several players are running down the tunnel, and then you hear the voice of the big guy (Jimmy broke his nose in the pool scene). Lots of players are running down the tunnel, yet when the big guy grabs him all you see are the players in the distance, when we should see loads more players running past Jimmy, Joe and the big guy. (01:21:35)
Continuity mistake: When Bruce Willis' daughter asks Damon Wayans to autograph his football card, he signs just his name. But when she looks at it the card reads 'To the daughter of the Last Boy Scout, Jimmy Wills', with perfect penmanship. There is no way he could have written all that. (00:58:00)
Continuity mistake: At the very end of the movie as Bruce Willis is talking to another character (I think its his wife I can't remember) the camera keeps switching between close-ups of Bruce Willis and the other character as each of them is speaking. Watch the cuts and bruises on Bruce Willis's face - each time the camera goes back to him the cuts and bruises very obviously change. They change between very severe damage to just slight scratches and light bruising.
Continuity mistake: At the police station, just after Cory was killed, the Chief of the precinct is looking at Joe and says "The same son of a b**ch saved the president's life." When the shot cuts to the other guy, then back to Joe and Jimmy outside the office, in the background the chief is now sitting back at his desk - some pretty quick moving between shots. (00:31:40)
Continuity mistake: Marcone goes into the parking lot, notices the white BMW, and shoots out the rear passenger window. The front window is now perfectly intact when previously it was shot at during the limo chase. (01:21:05 - 01:31:15)
Continuity mistake: When Mike's white car gets blown up, it spins in the air and lands the opposite way around, but in a following shot the car has now moved back to facing the same way it did before it blew up. (00:18:00)
Continuity mistake: The whole car lands in the swimming pool, with the back end stuck up in the air and the front end down because of the weight of the engine. A couple of shots later with Darian and the pool owner on the phone, the car is now sat up on its front end, which is now propped up on the side of the pool. (01:18:55 - 01:19:45)
Answer: You're right, I reviewed the clip. You see Joe holding the briefcase and Jimmy run out of the rich man's house, then get directly into his car. At no time do you see him putting the briefcase anywhere. It's most likely a bad editing job.