Acting for Two: Due to the briefness of the first part and the fact that they were supposed to be brothers anyway, some productions have the Ghost and Claudius being played by the same actor. Some see Hamlet's "Look here upon this picture"-speech as proof that this was Shakespeare's intentions and him lampshading it. Note that the guards hang around talking at the end of act 1 scene 1 just long enough for the actor playing The Ghost to jump into his Claudius costume for the start of scene 2.
The Royal National Theatre production with Simon Russell Beale had the actor playing Polonius doubling as the First Gravedigger, accompanied by some Leaning on the Fourth Wall: appropriately enough, given that Polonius was dead, the actor arose from a coffin to play the Gravedigger.
Word of St. Paul: The text of much of the notoriously garbled First Quarto of Hamlet is widely believed to have been reconstructed from memory by whoever played Marcellus in an early production, because all the scenes with Marcellus in them are closer to their counterparts in later editions, whereas whenever Marcellus is offstage the text starts to read like a best guess by someone who's witnessed several productions but has never bothered to memorise the whole thing. The 'mousetrap' scenes in the First Quarto are also very much as they are in later editions, suggesting that the actor doubled up (highly common in Renaissance theatre) and was in those scenes too.
Dawson Casting: Laurence Olivier was 41 when he played the title role. Eileen Herlie, who played Gertrude, was 30. The former was actually a pragmatic choice; with Orson Welles adapting Macbeth and also prepping for his version of Othello, Hamlet was the only other option and he had to cast himself as the lead to secure funding.
Dueling Works: With Orson Welles's Macbeth. Laurence Olivier had planned to adapt that but changed to Hamlet when he realised the other one would come out first.
Jossed: For years it was suspected that John Gielgud was the voice of Hamlet's father. It was just Laurence Olivier himself with his voice altered. Amusingly enough he would later play the ghost twice more.
No Stunt Double: The final scene to be filmed was the famous shot of Laurence Olivier jumping off a high tower onto Claudius and killing him, because it was considered to be so dangerous that it was feared that Olivier would injure himself too badly performing the stunt to film any other scenes. Olivier emerged uninjured from the leap, but the stuntman doubling as Claudius was knocked out from the impact and lost two teeth.
The Other Marty: Stanley Holloway was an 11th-hour choice; the actor who was supposed to play the grave digger, F.J. McCormick, died shortly before filming.
Real Life Writes the Plot: The reason the film is in black and white? Laurence Olivier claims "I was in the middle of a furious row with Technicolor."
Many actresses reportedly turned down the role of Gertrude because of "age concerns".
Claire Bloom auditioned for the role of Ophelia. She would later get to play Lady Anne in Richard III, Laurence Olivier's final Shakespeare film (directed by him anyway) and play Gertrude opposite of Derek Jacobi in a television adaptation of Hamlet in 1980.