I first tested the two features most important to me: exporting annotations and opening annotated PDFs from other apps. I saw that the first is not yet implemented, but that there is a menu item for it. I hope to see this soon. I was also able to open a PDF I'd annotated in GoodReader on iOS and have all the highlights listed without doing anything, which is great and bodes well for mobile integration with Paperpile even if the PP iOS app is a ways off in the future.
Personally I would like the annotation sidebar to be expandable. I have a large cinema display monitor and there is room to have more than such a narrow column. Or perhaps an annotation only view which is full width?
I like that one can search annotations, but something is needed to be able to more easily navigate and search comments as well. I suggest <> buttons that let you jump to the previous/next comment and a search bar at the top of the comments bar as well.
Finally, and this may be in your longterm roadmap, but it would be really neat if one could click on citations in a PDF and automatically add them to Paperpile with a note as to which paper they were found in...