Continuity mistake: While Sweeney is upstairs with Pirelli, Mrs. Lovett gives Toby a meatpie downstairs. On a closeup, half the pie is gone, but when the shot widens right after, only a couple nibbles are gone from the cake.
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)
Continuity mistake: The first time Judge Turpin is in Todd's chair, the shaving cream changes during this scene. When Todd lathers him up, covering Turpin's entire lower face with shaving cream, including covering the lips with a large blob of foam, but in Judge Turpin's next closeup, however, not only is the blob gone, but there is a streak at the corner of his mouth where it looks like someone wiped it away.
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.
Answer: His knife/razor/sharp edge to kill someone with.