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?
Continuity mistake: When Bond chases May Day up the Eiffel Tower, she throws the fishing rod at him and the wire wraps around his legs. As he falls down he has the gun in his hand. The next shot his hands are free and he is untying the wire. The next shot he has the gun in his hand. At no point does he put the gun down and pick it up.