I went to the Android Play Store on my Android phone and found the Salesforce1 App.  It shows a date of 3/17/2014 and includes comments --

What’s new in 5.1.1:
• Bug fixes and improvements
What’s new in 5.2:
• Custom Branding
• Bug fixes and improvements

But when I downloaded it , I get the Chatter icon, not the SF1 icon.  And when I run it and check the version it says it is "About Chatter Version 3.4.2 Build number 8".

Am I not getting the latest version?  Anyone know why?

For one thing, I'm only getting "Feed" and RECENT, not the other tabs I have configured including some custom pages under APPS.  All these work fine on iPad when pointing to the same org.