I'm having the same problem. It seems to be---from the commonness of this issue described around the web, as a search will demonstrate---to be a Snow Leopard issue. Some have thought it to be a MacBook issue, but while there may be some MacBook issue with the trackpad, this is not it; this is any mouse (Apple mouse, Logitech mouse, other mouses, cordless, corded, and trackpads).
I get the two issues you note: Dead clicks that just don't seem to go through, though sometimes it takes several clicks for the system to register the click; and the annoying click lock, where the system reads the MouseDown but not the MouseUp, which means it takes the click for a selection for drag and drop, and then when the mouse pointer moves, it carries a link or object stuck to it, or if it's reading it as the beginning of a text selection, extends a selection of text. Like... just now as I was typing this, and moved my mouse.
In addition to those, the pointer will stop moving or move brokenly, and get stuck and not move either right or left or up or down past some specific point it reaches.
This all does sometimes happen when a cordless mouse's battery is exhausted. But I have now changed batteries four times. It's not the battery.