Deliberate mistake: When Jack rips the door off the cab, he first breaks the top hinge and enters the cab. In the next shot when he pulls the cabbie out of the car, the door is completely off and laying on the ground. A few shots later when Jack grabs the newspaper, the door is seen hanging again.
Deliberate mistake: In the sequence where Jack finds his friend, and then the cards he is holding counts down to the explosion. Jack runs out, and the house explodes throwing the cop car into the air. If you look close, you can see the piston that launches the cop car and then falls back down.
Continuity mistake: When they are in the ambulance, Danny screams 'I said, turn around!' and draws his gun. The next shot shows the driver looking to the rear and getting scared by the gun. In this shot you can see by the window that the car is totally stopped, and some car with a yellow light is passing by them. But in the very next shot, the ambulance is stopping (you can even hear the tires) and there is no car with the yellow light to be seen.
Deliberate mistake: Just before Danny enters the action movie, Jack Slater (Arnold) arrives at his 2nd cousin's house. Jack exits his car and jams his desert eagle pistol into his waistband. He then approaches the front door where he turns toward the camera to kick in the door. You can clearly see there is no gun in his waistband now. In the next shot he draws the gun from his waist.
Other mistake: Before Jack's car jumps over the bridge, a van skids on the road. The first angle shows a thug firing at Jack, and the second angle shows Jack swerving to the left to dodge the bullets. The editing is all wrong here: The thug fires at the opposite lane to where Jack is, so he is really driving to where the bullets are.