Another bug I've noticed is that AMP breaks in-page searching with iOS Safari. If you perform an in-page search, the browser will not scroll to the found instances of the search term on an AMP page. I imagine it's related to the other scrolling issues.

Please, please fix this. It's impossible to support something that's foisted on us and breaks basic web functionality. If I were cynical, I'd say bugs like this are designed to degrade the web experience on iOS. There's a lot of bad web programming out there, but very few sites manage to break search.