Continuity mistake: When Zorin is trying to break into the shed where Bond is, just after he's worked out what time high tide is, the door rattles, dropping a hard hat onto the ground, but leaving a red/yellow light/reflector hanging, quite securely. The door lock is also pointing down and right. A couple of shots later, without the door being rattled forcibly again, there's nothing hanging behind it, and the door lock is pointing right.
Continuity mistake: When the bearded security guard attempts to punch Bond in Zorin's warehouse, Bond moves out of the way and the guard makes a hole in the crate. In the next scene, when several crates fall on the guard knocking him out, Bond has suddenly disappeared, and the hole in the crate that the guard has made is bigger than it was in the previous scene.
Continuity mistake: During the chase between Bond and May Day on the Eiffel Tower, May Day turns around and whips a fishing line at Bond which sends him sprawling over the rail. When he is suspended upside down halfway over the railing you can see his legs are wide apart, but when he regains his balance and starts to unwind the line, his legs are now bound together.
Other mistake: During the mine scene, we see Stacy Sutton in very tight miners overalls, then Mayday rips them off to the white dress she was wearing beforehand. There was not enough room in those tight overalls to hike up or bunch the skirt in any way for her to move her legs, or for her to have both legs in both pant legs.
Plot hole: When Bond and Tibbett break into the underground lab and find the device which drugs the racehorses, you can see that it has a large light emitting diode (LED) on the top of it. What possible use would that be, since the device is implanted in the horse's leg, and is supposed to be covert?