Stowe is driving a E34 BMW 5 Series (1989-1996) throughout the movie. Towards the end of the film when he takes off after Callaghan (who is holding his wife hostage), we see him drive his car right into one of Callaghan's cars...which was blocking his path. The camera gets a shot of him inside the car shifting the vehicle into reverse via a steering column shift. That particular BMW 5 series, or any BMW for that matter (aside from the new 7 Series which would only require a quick tap), did not have a steering column shift.
At the end when Callahan is holding Stowe's wife hostage in front of the helicopter, Callahan fires at Stowe once. When the camera comes back to him holding Stowe's wife hostage, we can see and hear her shriek as another gunshot is seen going off but not heard (the puff of smoke is clearly visible).
When Det. Anthony Stowe wakes up form his coma, he opens his eyes wide and they remain open as frozen. In a follow up shot, they are less open. And when his gurney reaches his house, his eyes are closed again. The opening of the eyes was the cause for him be to put in his wife's care at home, instead of staying at the hospital's trauma unit.
During the hostage scene at the end of the movie in the warehouse, as Anthony Stowe is driving his car towards Callaghan's men, the film crew is clearly visible on the right hand side through the windscreen.
The doctors say they took the bullet out of his head, as it was lodged in his skull. However when he is shot there is clearly an exit wound as blood bursts out of his head, implying that the bullet exited.
The goof item below may give away important plot points.
The movie is set in New Orleans, January 2006, clearly seen at the beginning subtitles. However, when Det. Stowe visits the tomb of his fallen partner Serge, the date of his death shown in the stone is 2003 (1977 - 2003).