My update is that it appears NOT to be happening any more, and I'm not sure why, or what changed. I'd sort of gotten used to it, but as I write this, I can't get it to recur.
Thanks for the suggestion. When it was happening, there was no difference in behavior whether the mouse is held down in "clicked" position with a lot of force versus a "normal" amount of force. I believe it's a software issue. I tested the same mouse with different machines running Snow Leopard, and I have yet to replicate the behavior on them. I think it had something to do with my machine (Mac Pro) running Leopard, using a mouse that was designed, I believe, with Snow Leopard in mind. I'm still using Leopard, but at the moment it's not misbehaving.
I'm surprised I couldn't find anyone else having the same issue (aside from Michael Spryn above), after some extensive Google searches.
Weird annoyance, but seemingly gone for now.