Unlike most period films, this one was shot almost entirely with a hand-held camera. The two most notable shots with a fixed camera (not a hand held one) are the two panoramas of the interior of the theater, which was intentional.
The poem which Wilmot has been banished from court at the beginning of the film is "A Satyr on Charles II". The historical Wilmot really did submit that poem to the monarch accidentally, but he subsequently left court of his own accord, rather than at Charles' command.
In several shots, the fake nose John Malkovich is wearing is noticeable, including the sun glowing through when outdoors, and when in the theater box speaking to Johnny Depp, there is a distinct color mismatch that shows the outline of the prosthetic.
In the playhouse, after Harris announces the kings arrival, Lord Rochester starts to remove his hat with his right hand on the crown of the hat. In the next shot, he is removing it with his left hand on the brim of the hat.
When Rochester returns home, the carriage gets stuck in the mud so he gets out and walks towards the house. He's met by his wife. Rochester says, "Madam. This driveway will not do." The word "driveway" didn't come into use until around 1865 (according to dictionary.com) - about two hundred years after Rochester's death.