Continuity mistake: After Mrs. Lovett says "A customer!", the knife she stabs on the counter and the blob of flour change positions.
Continuity mistake: When Sweeney kills Turpin, his forehead is covered in blood. Half a second later there's just a tiny spot.
Continuity mistake: During the "Worst pies in London" song, Mrs. Lovett drips the pie filling into the crust, and it fills the crust up to a bit over the top. In another shot, she rolls on the pie top, but the filling is much less than before, not even to the top of the crust.
Continuity mistake: Anthony's backpack during the I feel you secene keeps changing positions: Under the bench, slightly out, totally away, etc.
Continuity mistake: Just after Lovett finishes singing "Wait", Anthony comes running up the stairs and Sweeney hides behind the door holding the razor in his right hand. Anthony turns to Sweeney to speak, and Sweeney places his right hand on Anthony's back and guides him toward the window. You get a glimpse of the closed razor. The camera instantly changes to looking at Anthony's back,and Sweeney's hand is empty and fingers are spread out. When the camera angle changes again and Sweeney sits Anthony down, you get a quick glimpse of the razor in Sweeney's right hand. (01:13:00)
Continuity mistake: At the beginning of the song 'a little priest' Mrs. Lovette is holding the curtain and opens it. When the camera switches, the curtain is fully closed and she's just holding a little bit of the curtain.
Answer: From what I heard, the chorus songs (known as "The Ballad of Sweeney Todd") were cut due to time and inability to make the chorus work on-screen. Actors were set up to play "ghost narrators" at first, so that indicates that the filmmakers did want to include the songs. They were just not able to find a way to make them work satisfactorily for them. Also, I think (can't verify) I also heard that Stephen Sondheim, the show's original creator and composer/lyricist, agreed that these cuts needed to be made for the film to work.