NOTE: This post was written during the time of Google Play Books version 3.1.23 (30123). In the future, this post may quickly be rendered obsolete and unnecessary, depending on how fast Google decides to fix the problem. In the meantime, if you use the aforementioned version and below, this fix could help you.
I've started taking a liking to Google Play Books and was immediately impressed by the fact that I can upload my own .epub files onto the app, and that .epub file will be available across all of my Android devices where GPB is installed and my Google account is logged in. It even syncs the last page where I stopped on one device, so I could continue there on another, though this feature is still sketchy, as I observed that I had to "move" out of the book by pressing Back or Up so that it could sync.
Anyway, the uploading feature is really nice that it made me use my Kindle less and my Nexus 7 (and Nexus 5) more, because Amazon only syncs books that were bought in the Kindle Store, plus the Amazon reading app for Android is very lacking when compared to Google Play Books.
However, there appears to be a problem with uploading: After uploading, GPB will begin to process the book, displaying "Processing" on top of the book's progress bar. Then it would stay that way, possibly forever. I left mine processing an EPUB of Dante's Inferno for six hours and it still wasn't done.
I tried all sorts of solutions, including rebooting my tablet, which is really unnecessary, but you know what they say about restarting things. Then while GPB was on a Processing loop on my tablet, I checked my phone, and guess what, they were already uploaded from the phone's side. I then came to the conclusion that Google Play Books was already done processing the files a long time ago, and the UI didn't respond with a refresh after the processing.
Therefore, the fix is simple: Wait for a minute or so for the book(s) to process, then tap Menu > Refresh. Google Play Books should query the cloud again and receive the confirmation that the books were already done being processed, and your book(s) should be ready. If that doesn't fix it, just wait a little more before refreshing, or reupload your books.
Hopefully this should help people who are stumped with the uploading books on Google Play Books. It's a great ebook reading (and acquiring) app, especially with its sexy 3D page turn animations and clean UI, if not for the lack of customization for one's reading options. Hopefully this workaround could escalate the problem to Google so that they could fix it sooner as well.