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.
Dawson Casting: MAD joked that in the 1990 film version, Hamlet and Gertrude seem to be the same age. While not quite the case, it is bizarre to have Mel Gibson - 34 at the time of production - play the son of then-43-year-old Glenn Close!