I grew up with Dr. Who, I enjoy the show, and I laughed my socks off during "The Curse of Fatal Death"
The piece tries to amuse both long-time fans of the show, and casual viewers who only know it 'that cheesy British sci-fi show', so it has a fair bit of juggling to do. However, the the comedy draws from both ends of the spectrum and, I think, can provoke laughter from anyone who has a passing familiarity with the original.
All of the actors (Atkinson, REG, Broadbent et al) manage to put their own mark on the character during their brief interlude as the Gallifreyan Timelord and seemed to have fun doing it. Pryce was clearly having far too much fun hamming it up as The Master. Pryce's comments about prepping for his role make watching the 'making-of' segment on the video worth the time, alone - and the rest of it is quite entertaining, too.
Granted, the humor can be a bit broad, but this isn't a subtle social satire, folks, it's a blatant parody and, as such, some silly things are going to happen. I've heard rumbling complaints from purists about CoFD being "disrespectful" or something and I think that mayhaps those fans are taking themselves too seriously. If you can't laugh at yourself, then it's probably too late for you...