I myself had trouble because the app first wasn't available and then wouldn't install on my Hisense Sero 8 tablet (it still won't install), but I did manage to get the app installed on my OneTouch Pop Icon smartphone this morning. This offers a unique opportunity to compare the content available in one app versus the other, and other differences.
For example, what B&N didn't tell us was that the Nook 4.0 Android app now supports the videos which B&N sells on its site. You used to have to install a standalone Nook Video app to watch the videos, but now it is no longer required. The new app also supports enhanced ebooks. I recently acquired an ebook with embedded video, and I can watch the videos in the new app on my smartphone (but not the older v3.5.3 app on my tablet).
And finally, the app does have a different home menu and library menu which better organizes the diverse types of content now supported. I'm not sure I'd call it an improvement, though; the older interface was easier to browse.
Aside from the new menu and support for video and enhanced ebooks, the apps largely have the same features (they're just organized differently). The margin, background, line spacing and other reading options are identical.
The new app doesn't support audiobooks, so far as I can tell, and both the old app and new app support magazines, newspapers, and digital comics.
All in all, this is going to prove convenient for anyone who buys a lot of different content from B&N. You can find the app in Google Play.