Continuity mistake: When James has just jumped out of the plane, he has a diving rig that is somewhat different to the one he has when diving on the wreck of the Devonshire. In the water he wears a twinset manifold air-bottle rig. While skydiving the rig was not manifolded and the bottles were in a different position on his back. To change between the two requires some work with a tool kit, preferably on dry land.
Continuity mistake: Near the beginning when Bond causes mayhem, he sticks a grenade onto a moving vehicle and dives off it. As he jumps off and attacks a bad guy his collar is up (to better hide the face of the stuntman), then when it cuts back to a proper shot of him his collar's suddenly down. (00:04:50)
Continuity mistake: There is a shot from behind a video camera, showing a wire or cable coming out of the back of the video camera, however, in all subsequent shots the wire/cable is not present. (00:00:50)