The largest complaint by far is that the URLs for AMP links differ from the canonical URLs for the same content, making sharing difficult. The current URLs are a mess.
This is something that the Google gang are aware of, and they say they’re working on a fix. But this post points out some other misgivings with AMP, like its governance policy:
This keeps the AMP HTML specification squarely in the hands of Google, who will be able to take it in any direction that they see fit without input from the community at large. This guise of openness is perhaps even worse than the Apple News Format, which at the very least does not pretend to be an open standard.