Is the difficulty in Typing of the Dead dynamic?

You're absolutely right! It's wholly dynamic. If you never took damage or had to use continues, the difficulty would climb and climb until you always had to type a long sentence in. The way I remember, it lowers a little with single lives you've lost (i.e. taking a hit) and drops considerably after continues.

The tranquilizer is also supposed to have such an effect. No reason to believe it doesn't.

Oh and the path you chose doesn't directly affect the difficulty, but you can be led to slightly different boss fights, i.e. several bosses have types A and B one of which could be tougher to beat than the other. But that's unrelated to the first point.

I used to play the game a lot so I'm fairly sure of this.