Continuity mistake: When the the old Asian guy is about to draw a picture of an atomic bomb on his blackboard, he clears a small section at the top of the board, and you can see some diagrams uncleared in the centre of the board. Yet when the camera shows his picture, the diagrams in the centre have now magically disappeared.
Continuity mistake: In Khan's lair, when the Shadow is struggling to stop the Phurba from attacking him, the Shadow is dragged across the floor by the Phurba while holding it in his right hand. In the next shot, he is now seen holding the Phurba with both hands.
Revealing mistake: After Shiwan Khan's goon falls to his death and Moe is looking at the dead body, it is elevated up to the mid-section of Moe's body, indicating the the body was on a table or platform to get a better camera angle of Peter Boyle (Moe) observing the dead body. The shot could not have been accomplished if the body was at ground level.