Continuity mistake: When they find out Lecter is on the elevator, they look down the shaft at him and there is quite a lot of blood on his back, so much that it even reaches down to his belt. However when they open the elevator shaft and the body falls down, there is only a small amount of blood on his back.
Continuity mistake: While travelling from the post mortem examination, Clarice is in the back seat speaking to her boss. In going back and forth in conversation, her hair changes from being curled up to being curled under, all in one swift change. This is a different style and not done as could be by running your fingers through your hair as the camera cut away.
Continuity mistake: When Lecter is in the ambulance, wearing another man's face, as the ambulance officer has his back to Lecter, Lecter takes the large dressing off his face and pulls the oxygen mask down, then sits up, but when he does, the oxygen mask would be in the way; it is around his neck, he would have had to pull it over his head to get rid of it, but he didn't do this - the oxygen mask vanishes.
Continuity mistake: When Lecter is in the Memphis jail cell, trying to escape, there is a shot of him eating the face of Sgt. Pembry, and a nano-second later, you see Lecter trying to completely shove the jail door on him. No way these two events could have transpired so quickly.