What's it mean when I press an application on the home screen and instead of opening it the little tray at the bottom of the screen bounces at me? This seems random. The answer is probably obvious, but thanks in advance.
It means you are touching/pressing the icon too long. A tap opens the app, whereas a long press activates the move/drag mode. The Droid thinks you want to move/drag the icon, that's why it "bounces" or wiggles. The tray button will change into a trash can so you can drag the icon over it to delete it.
Try shorter taps/presses on the icon.
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