I just got this app and the iPod yesterday. What happens is that if you're in a book and you start jumping around, it doesn't seem to remember your last page. (use the bookmark feature, even though you shouldn't have to) But if you're reading and simply hit the button to leave the app and go back to your home screen, it does remember your place when you restart the app.
This should be quite an easy fix for Amazon. I'm going to shoot them a note when I get a chance.
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