When you have a mouse whose scroll wheel doesn't work, you tend to use the scroll bars a lot more. I usually click the little arrows at each end repeatedly as I read the page. This means that I'm not looking where I'm clicking, and so my mouse tends to wander slowly, which results in me clicking stuff I didn't mean to.
A simple way to fix this—and it applies to many elements of a computer's graphical interface—would be to move the mouse pointer to the middle of the button when you click it.
This should be done when the mouse button is lifted, and only to controls that afford repeated clicking. So menus and drop-down list boxes would be excluded, because just clicking them does nothing and they can be dragged to select an item (in Gnome, anyway). Buttons that dismiss dialogue boxes, and the Minimise, Maximise and Close buttons in windows' title bars would be excluded as well, because the buttons move or disappear after you've clicked them once. Tabs; buttons that bring up a new window that you're expected to interact with straight away; and radio buttons (“choose one of several”-type options) wouldn't be included, because you don't need to select them twice in a row.
But tick boxes would, as you might want to toggle them. Most toolbar buttons; program launchers (on Gnome's panels); those little up and down arrows next to inputs that want a number; toggles for expanding to show more information; and scroll bar buttons would be included, too.