Google have updated the Android version of Google Play Books. The new version has an improved UI and Google say they have fixes over 90 issues. There is still no way of importing books in to the app so I will continue using the Kindle app for now.
What’s in this version:
Fixed over 90 issues, including crashes.
Implemented a number of UI improvements, including an added drop-down menu in the library to filter books by type, and identifying place names on the current page when the reading controls are showing.