When filming the scene where Caligula asks Claudius if he's mad, neither Derek Jacobi or John Hurt could keep straight faces. Hurt later admitted that the two of them only managed one take where they didn't both burst out laughing, and this is the take that ended up in the episode. Even then, when the camera focuses on Jacobi his eyes are crinkled with trying not to giggle.
This episode takes place from 40 to 41 AD.