When you go to costumes,check all of them and make sure they are EXACTLY in the middle. You can move it with this tool, if its not in the center.
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If you "Go To" another sprite, the place you go is the "rotation center". You can change this point using the sprite editor. It doesn't have to be in the middle of the graphic part of the sprite, and can even be completely off the graphics. It sounds like this is what you have happening.
-MrEd
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