Other mistake: At the end of the song "Wait," when Sweeney and Lovett hear Anthony running up the stairs, Sweeney runs behind the door to his shop. For a quarter second, as Sweeney places his back against the wall, there is a modern-day water bottle on the window ledge. This, however, cannot be seen on the DVD or Xbox, though on laptops and probably computers also, when streaming you can see it around 00:43:10. (00:43:10)
Other mistake: Based on the location of the barber's chair with the picture window in Todd's barber shop and the layout of the exterior of the building, there is no possible way that the chute behind the chair would be able to dump the bodies directly into the basement without going through the center of Ms. Lovett's shop.
Answer: His knife/razor/sharp edge to kill someone with.