I must be missing something.
No. The good bombs will influence your test particle differently than the bad bombs. Zeno principle at work.
No, because in the case where the photon appears at detector C, and the bomb remains unexploded, the photon never actually hit the bomb. The wavefunction takes both paths, but the wavefunction is not the photon. The wavefunction is a description of possible paths (or locations, if you will) for the photon. If the detector at B isn't working, then there's no way the photon could ever end up at C, because the wavefunction that describes its allowed paths would cancel out. The two paths to C end up with the opposite phase by construction.
So we see a photon at C, and we see no explosion. What do we know? Well, we know that the detector at B works, else we couldn't have seen the photon at C. (The photon would necessarily have taken both paths, you see, leading to the wave cancellation at C. But since in the exploding case it can't take both paths, the wave cancellation at C never occurs.) We also know that the photon took the path that didn't go past the bomb, or the bomb would have exploded. So we know that although the bomb didn't explode, it must be good.
[Geek alert: the "photon", as we use the term here to describe the thing that makes the bomb go boom, refers to the position eigenstate of the wavefunction. Careful, though: sometimes the word "photon" can refer to the momentum eigenstate of the wavefunction (as in, "what was the frequency of that photon"), and sometimes it can refer to the wavefunction itself. In this example, though, what matters to the bomb is where the photon goes.]