This one has been bugging me for a while, so thanks for the kick in the pants. 
Turns out the problem is the sprite's "here's the area of the screen I've drawn on" record doesn't get cleared when it moves offscreen. I've added a fix for that, but we'll definitely want to test it thoroughly before pushing it--if I screwed up and I'm clearing that record in cases where I shouldn't be it'll leave garbage pixels on the screen.
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