For a property so utterly theatrical, I thought Burton did a pretty good job of solving the inherent problems of translating it to the screen. Perfect? No. But successful storytelling, yes.
I thought there were HUGE editing problems and SBC and HBC were horribly cast but i still enjoyed it's faithfulness to the stage show. I ended up seeing it around 3 times in the theatre. I loved the live singing and i wish more movies would do it.
the thing I enjoyed most about the movie version was the orchestra...it was so awesome to hear the SONDHEIM score played with a full orchestra...the way it was intended to be heard IMHO...I hated the later John Doyle, everybody sings and plays an instrument version...
I liked the Sweeney Film, and agree with what Wilmingtom said: Sweeney Todd is a pretty theatrical piece, and I think Burton did a solid job of reshaping it for the screen. Any film adaptation of the show was bound to have cuts and alterations. By definition, that's part of what it means to adapt a work into another medium. Now whether or not those alterations work for the film, is up for debate. In my opinion, most of the changes for Sweeney Todd worked.
And actually, the changes for the film weren't nearly as severe and sweeping as they might've been. I remember hearing rumors before the film started shooting that 'Wait' was being cut, and Sacha Baron Cohen's Pirelli was going to be rapping (lol!).
While I agree that a lot of the humor in A Little Priest was removed, the film did have a few humorous moments - the By The Sea sequence, for instance.
"You drank a charm to kill John Proctor's wife! You drank a charm to kill Goody Proctor!" - Betty Parris to Abigail Williams in Arthur Miller's The Crucible