That is weird. The kindle app is far from my favorite reader app on the iphone (I prefer Stanza by far) -- but I don't have the problems you describe. Mine always opens to the page I was last on.
Is is possible that you are sharing your account with someone else? If they are reading the same book you are -- on the same account -- the app opens to the latest spot reached by either device. This is a feature you can turn off.
I just wished that feature worked better. When switching between my iPhone and iPad that syncing doesn't always work.
Lee
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