The only related issue I've noticed is that after riding in the rain, there is a small amount of water that traps in the same place you describe. I might try the gasket Miles mentioned. I also thought that a very thin bead of clear caulking or weatherstrip could work as well.

So far, I've only seen a very small amount in a very small area. There's just enough that you can barely change the shape of the wet area by pressing on the base of the windshield. I hadn't given it much thought, but now that you mention it, I assume dirt/grime could collect there as well.