When they go into the police station, just before Robert Patrick walks out Sharon Stone walks out in her Basic Instinct outfit. Another nod to the "movie within a movie" concept. See more...
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Continuity: 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": 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.
Other: 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.