What I would like: an "export PDF with annotations" option (perhaps in the "Tools" menu?) that opens up a save dialog and, after you pick a file name and folder location on your hard drive, creates a copy of the PDF there with all annotation included in the native PDF annotation format.
In this case the file menu IS intuitive, once you know it's there, but it's still not AS intuitive as right clicking or looking within the PDF itself. Adding it to those locations, too, would indeed be useful.
I often find that many functions are located in menus that aren't necessarily intuitive (copy citation/bib under edit, for example)