As Claudius and Gertrude welcome Hamlet back to Denmark in the throne room, the ladies to the side change places.
When Hamlet and Polonius are walking down a hallway discussing Hamlet's sanity, in one shot Hamlet is holding a skull mask, and in the next it's gone.
When Laertes is shouting at Claudius on his return it is shot from two angles. From Claudius' view Laertes' sword is pressing against his neck and he pushes on it as he speaks, but from Laertes' view his sword is not touching and he waves it slightly as he speaks.
Gertrude and Claudius are standing in different positions depending on the shot.
The snow on Hamlet's boots and Rosencrantz's trousers, plus the cane disappear as they enter the castle.
There is an electric cord visible coming out the back of a lamp on a table near the window during Hamlet's long soliloquy in his chamber. However, as Kenneth Branagh deliberately made the film non-contemporaneous, including the use of a steam train, this may not have been accidental.
Fillings can be seen in the teeth of Hecuba (Judy Dench).
In the very long shot along the length of the throne room, the cameras are visible in the mirrors.
After Hamlet speaks with his father in his woods, while he runs and is met by Marcellus and Horatio, there is a quick pan shot in the woods where you see a ladder covered by a long board on the ground.
Light stand visible in the mirror just before and during a soliloquy.