It's very difficult to do a broadway performance in movie format. IMO...most movie musicals are pretty hokey unless they're in animated format. (Disney)
Cats was done as a movie, which actually was quite good. It has some of the original cast. If you can, get the video that shows the audition and thought process of Andrew Lloyd Weber. Although, it wasn't as exciting as the live show (which I've seen 3 times), you won't be disappointed. It was definitely ALW's baby and you can see how attached he is. The story is kind of strange but once you get used to the factions, you can see how it is a very human story.
Here is the Wiki on Cats:
http://en.wikipedia.org/wiki/Cats_(musical)
Another that wasn't done badly is Rent. I was really impressed how that one came off. The problem for me, is that I'm a Broadway/Off Broadway purist. Seeing a live show is an organic experience and really cannot be replicated.
http://www.imdb.com/title/tt0294870/