Ok… I get little pink dots on my grid while i’m working, and whenever I try to resize/rotate an object, the object uses the dot as it’s center point. What creates these dots, and how do I erase them?
You can’t erase them, they mark the object’s centre point (though they’re quite often not in the centre).
You can snap it to the centre of an object by selecting the object, going to the editing buttons (F9) and selecting “centre new” (in the “mesh” panel).
Hope this helps.
to prevent having to do that, make sure you EXIT out of edit mode before you move the object. when you move in edit mode, you are changing the center point.
You can change the size of the object centers in the preferences, too, in the first tab, near the settings for the size of the 3d manipulator widget.
I’m not sure if you can make that size zero, though. 
Well making it invisible wouldn’t solve the problem - it would just be more frustrating. Like spiffyandy said, just be careful not to go moving things around in Edit Mode (I’m sure most of did this in our early days) - and like animatinator said, just put the center back where you want it for more rational responses for size and rotation.