If there's one thing that's kept me from using Feedly's official app, as opposed to using more conventional RSS-style readers in the wake of the Google Reader collapse, it's the interface. Aside from the fact that I find it kind of clunky in general, the inconsistent back button behavior is a real downer. With the latest app update (version 18.1.3), it becomes a little bit less of a headache.
Now when you go through the various screens you've viewed with the back button, you'll open the "level selector" (read: the swipe-out side menu that shows all your feeds). Tap the back button again to exit the app completely. That should cut down on the instances of accidentally closing out of the app after reading a single item in a feed.
You can also go to the next feed in your master list once you've finished the unread items in another. Formerly you had to go up one level and select a new feed, now you can just use this handy "load next selection" button once you finish the active feed. Nice.
Feedly is still missing some of the more conventional reader features, including a standard scrolling widget, but these new additions should please those who prefer the swiping interface. The web version of the Play Store still lists the app under version 18.1.2, so it may take a while for the update to go out to all users.
Update: It looks like the 18.3 functionality is only in the beta. It should be pushed out to regular users soon. Thanks to commenters bozzykid and BigTimmay for the heads-up.