The situational criterion for monologue is that there is no addressee, at least not on stage. This kind of monologue is non-existent in Sweeney Todd excluding the Ballad.
The structural criterion refers to the length and autonomy of a particular speech. When we use this criterion to label monologues, we can find several good examples of this in Sweeney Todd: My Friends, Epiphany, The Contest etc.
Then there is of course the distinction between soliloquy and monologue. I believe the main difference between them is the fact that a soliloquy is not meant to affect others, and a monologue is. The soliloquy will be discussed in more depth later on.
As we can see, the distinction between monologue and dialogue is not always clear. Many verbal utterances can be perceived as a mixture of the two. The Epiphany provides us with such an example.