Visible crew/equipment: When David Mann stops off at the reptile lady's place, he enters a phone booth to call the police. When he's inside, you can see a perfect reflection of Spielberg. Look how young he looks.
Deliberate mistake: The famous car chase ends with Bond's car tipping up on its right wheels to fit through a pedestrian path. However, when it emerges the other side, it's tipped on its left wheels. When the car enters the alley, this was filmed in a studio. When the car exits the alley, this was filmed in Vegas. The first few times the exit was filmed, the car emerged on the correct wheels, but the shots were unusable because of the crowds in the background watching the filming. This shot was temporarily abandoned and eventually re-filmed with a different stunt driver who famously performed the stunt on the wrong wheels. Realising this, the producers filmed a somewhat clunky insert shot featuring a close-up of Sean Connery and Jill St John, which shows the car tip back onto four wheels and then up onto the opposite two wheels, even though the alleyway would be too narrow to manage this.
Visible crew/equipment: When Bumpy hires Shaft to find his daughter, Bumpy gives Shaft an envelope with money, and when Shaft stands up you can see the bulge of the hidden microphone and wire at the front of Shaft's turtleneck sweater. When Bumpy leaves the office Shaft turns around and there's a bulge at the back of his waist, which is presumably the mic transmitter. (00:26:10)
Visible crew/equipment: When the Mayflower truck crashes into the police cars, crew members and the second camera (presumably filming the stunt from the overhead angle) can be seen in the wideshot at the left side of the screen, before the camera pans to the right for a close-up of squad car 351.
Continuity mistake: At the police station, Cloudy takes the cigarette out of his mouth. A shot later, it's back in. (00:34:56)
Continuity mistake: When Alex is informed that he's being transferred to the Ludovico center, the governor's arms jump from his lap to under his chin, then back to his lap. (01:06:00)