The song list above is based on the production's playbill listing, but we've added extra identifying information for several numbers — the opening and finale "Ballad"s, the two songs titled "Johanna," and what was listed in the playbill as "Quartet," which many productions don't list as a separate number. In addition, we've listed the organ prelude, which was not listed in the playbill.
Some things that may seem odd — e.g., not listing Todd in "By the Sea," listing the Beggar Woman in "God, That's Good!", listing Johanna next to last in the "Final Sequence" — reflect the listing in the playbill.
Only the opening and the closing "Ballad of Sweeney Todd" were listed but none of the other reprises and variants of the number. "The Letter" was also not listed.
Despite what Sondheim has said in two books — Sondheim on Music: Minor Details and Major Decisions and Finishing the Hat — the tooth-pulling sequence in "The Contest" was in the production for the entire run. One section of "The Contest" was cut during previews; specifically, Pirelli's opening section of the number (the section starting "Now, signorini, signori" and ending "Pull all of 'em out!"). That section was, however, included on the cast recording. This is how that cut worked in the production: After the Beadle said, "The fastest, smoothest shave is the winner," there was a brief musical transition, then Pirelli sang "To shave-a da face" and continued from there with the rest of the number.
The first half of the "Now, signorini, signori" section (with one minor lyric change) was restored for the London production and the national tour, both of which cut the tooth pulling. Many productions since have followed their example.
The cast recording shortened the organ prelude. On opening night, an even longer version was heard, but a cut was soon made that nonetheless left a version that was a good deal longer than what was heard on the cast recording.
Also heard on opening night was a different lyric for the end of the final reprise of "The Ballad of Sweeney Todd." This lyric, which was heard during previews and through the weekend after the opening, was:
Sweeney: To kill for love is such a thrill
Mrs. Lovett: You don't even notice you lose what you kill
Company: Like Sweeney,
Like Sweeney Todd,
The demon barber of Fleet Street.
Some online sources incorrectly list the number of previews as having been 19. The correct number is 27, at least if you include the performance that wasn't completed because of a scenery malfunction during "City on Fire" in the second act. Since the performance was only about 15 minutes from the end when it had to stop, we are counting it.