Continuity mistake: When the two guards go down the stable elevator to the laboratory, the amount of straw on the floor of the elevator changes between shots.
Continuity mistake: When Bond meets Stacey for the first time at Zorin's reception, he hands his bottle of champagne over to a waiter. At this point, you can see a Chinese couple walking behind Bond and Stacey, but in the next shot the Chinese couple have disappeared and another couple walk by that weren't in the previous shot.
Continuity mistake: When General Gogol is in M's office at the end of the film, he is holding an Order of Lenin medal in his right hand, but few shots later he is holding a glass of champagne and the medal is nowhere to be seen.
Factual error: May Day eludes Bond by executing a base jump from the top of the Eiffel tower. Bond then chases her for several minutes before she finally lands on the boat on the Seine river. The problem is that a base jumper from 300 metres (the height of the Eiffel tower) will only take about 30 seconds to reach the ground. Bond would not even have had the time to descend from the tower in the elevator before she would have landed.
Character mistake: In the pre-credits sequence, when Bond is fighting the Soviet troops who are attacking him, Bond hooks a grappling hook onto the back of a Soviet soldier who is a riding an snowmobile, which sends the soldier flying off the snowmobile and hanging over an icy ledge. The soldier then says "Pomageete! Roger Moore pomageete!" which is Russian for "Help! Roger Moore help!"