Revealing mistake: During the draining of the water in the dish, some shots show the water moving backwards. For instance, at a particular moment, masses of water jump UP, ark toward the opening, and fall in it. The most likely reason is that, during the filming, the special effects people took a shot of a replica of the dish FILLING with water, then edited it the other way, to show that the water was emptied from the dish.
Revealing mistake: In the scene containing Q describing the operation of the "grenade" pen to Bond, Q is not looking at Bond and appears to be being cued. With careful observation you can see Q's eyes reading the cards. Also, his actions/reactions do not seem fluid but abrupt as he reads to a point where he must do an action of some sort and he performs it suddenly. Much of the scene is shot from a profile view of Q and Bond so as to reduce the obviousness of it (mostly during the longer dialog pieces for Q).
Revealing mistake: At the beginning when Bond is chasing the plane on the motorbike, in the last shot of Bond from behind before he goes over the cliff, the background shot of the mountains is a painting. Not only can you see the square sections on the wall, but some parts of the painting don't even match.
Revealing mistake: During the shot where Bond and Alec are emerging from the hallway floor in the dam compound, watch the left wall. As Bond bumps against it after pulling out his pistol, it visibly flexes inwards and pops back out. A concrete wall capable of supporting the weight of a dam with industrial-grade pipes wouldn't flex in like that; it's quite a thin wooden set made up as such.