Although I had read that the movie was a fairly straightforward adaptation of the original musical, Tim Burton made the choice that the actors would sing without reaction from anyone they interacted with (unless the other character was also singing). I think that is probably a good choice to make for a film of this material, but I was disappointed to lose the chorus numbers, like The Ballad of Sweeney Todd, God That's Good, and the haunting quintet on The Letter.
I also was slightly disappointed that they truncated some of the numbers, like By The Sea, although again, I can justify the decision to do so because the reason some of those songs are included at the length they are in the stage show in the first place is to accommodate set and costume changes, which were unnecessary for a film. I can't say that I missed the lover's frantic duet or the extended version of Pirelli's Miracle Elixir.
Johnny Depp and Helena Bonham-Carter both delivered very good performances, acting-wise. One complaint that I've had at various productions of Sweeney Todd is when Mrs. Lovett is turned into some kind of sex maniac. Yes, Mrs. Lovett desires Sweeney, but it's all delusional: she desires a man who doesn't exist - she imagines some sort of normal life for them, but Sweeney is broken, possibly irreparably, before he ever walks into her meat shop. They avoided going down that road in the film.
I thought Alan Rickman was quite good in his role as Judge Turpin. He's a sick man, a predator and capable of great cruelty, and yet sees himself as a trully moral man - he has that kind of self-delusion that a lot of powerful people seem to have.
Sascha Baron Cohen provided both comic relief and some menace as Pirelli. Ed Saunders was Toby, and I'm not sure they could have cast the part more perfectly. He had a baby face and that sweet unchanged voice, but also deftly portrayed that Toby had experienced a hard life and didn't have high expectations for the future.
The story of the lovers got short shrift in the film, which I think was a good choice. Jayne Wisener as Joanna looked like a doll, but as in the stage show, she is less naive than her would-be lover, Anthony Hope. I thought Jamie Bower's voice was a little thin and reedy for the part, but when he sang in the Joanna reprise, I could understand a little better why they cast him, since his thin and reedy voice made Depp's sound positively beefy.
No one else I was with noticed, but there was a cameo by Anthony Stewart Head (causing me to squee: GILES! Although only silently, because I am respectful of others at the movies). Which makes me disappointed that they didn't have him sing anything.
On to the singing! My main complaint about Depp's singing is that too often, he closed the vowel, e.g. "I will have vennnngeance" instead of "I will have veeeengeance", which is sort of a general no-no when singing in a non-rock/non-pop style. That wasn't enough to detract from what was overall a terrific perfomance. He captured the emotional resonance of the character so well.
Bonham-Carter had fairly poor breath support - there was a lot of swooping to the right pitch, and breathiness, and she didn't really hold anything out, but her voice had a sweet clear tone. She did handle the patter of Mrs. Lovett's songs well, and I could understand every word.
I was underwhelmed by the presentation of A Little Priest. Although the choices Burton made can be defended, I didn't feel exhilarated at the end, as I usually do. I did like the nod to the blocking of the original production, though, with Todd and Lovett holding up their "weapons": a butcher's knife and a rolling pin. I would have preferred a more vigorous presentation, but I didn't direct the movie, so all I can do is tell you that in my head, it's a lot more exciting of a number.
The orchestrations were great - they are reason enough to buy the soundtrack. The songs and chorus parts that were cut are in the orchestration, so if you are anything like me, you'll sing along where the movie does not.
All in all, it was a worthwhile adaptation of what is possibly my favorite musical. Not perfect, but very good.