Here is my check list for upgrading sites from Media 1.x to Media 2.x.
1-Disable Media 1.x and File Entity 1.x
2-flush cache
3-Install Media 2.x and File Entity 2.x
4-Enable File Entity 2.x
5-Flush Cache
6-Enable Media 2.x
7-Run update.php
8-Cross fingers :)
9-If all goes well, go into the database and replace all pdf, doc, excel file types from "default" to "document". Find "types" in file_managed table. You can leave them as default, but "document" type is what Media 2.x automatically assigns these types of files.
I really didn't have any issues on my sites going from 1.x to 2.x using these steps, most of the bugs in previous version of Media 2.x seem to have been resolved.
For sites using Media 2.x-alpha, I assume is just a normal upgrade. For sites i had with Media 2.x-alpha I had to run a drush rr (registry rebuild), because all our sites are part of a single multi-site installation, so those running Media 2.x-alpha had their own copies of the modules, and i was moving them back to using the Media module in the sites/all/modules folder so the registry rebuild I believe just found the module in its new place. If for some reason your media gallery is not picking up the right image type, you might have to manually go in and create "square_thumbnail" ... i had to do this when i tested it locally, but not on our dev and staging servers.
All this is fairly well documented here: