I understand that the U.S. has accidentally dropped bombs on ourselves many times without actually detonating the bombs. These accidents have caused craters, but no radiation (or in a couple cases, just a 'little radiation' that leaked into soil, etc). An easy google search will tell you more. 

We've also accidentally transported armed nuclear warheads without realizing they were armed (see R. Maddow's book 'Drift')

But for my specific question... is it remotely possible that after a nuclear bomb has been dropped by accident, it could then detonate? That is, create a mushroom cloud?

If so, how? How would the failsafes fail?

WHY THIS IS WORLDBUILDING (because there have been complaints)
I'm literally building a world in which such a thing could happen. I'm writing a novel where we have a different president, a slightly different governing system, and more or less the same military, but slightly more incompetent than it currently is. This world will reflect on our current world a good bit, but it differs a lot. 

In the novel there is a nuclear detonation in the U.S. that is basically the U.S.'s own fault... want to figure out a way that it could believably happen)