Android 5.1.1 Xperia Z3:
Note: this may not work for some "magic" apps, like the Play App itself.
Settings > Apps > Downloaded > App name
and the version is shown at the top of the screen.
I was not able to search by the app name, so get ready for some scrolling.
Running instead of
Downloaded did not work: if you find your app there, it shows only runtime stats.
Better method if you've got it setup.
Discussed at: http://stackoverflow.com/questions/11942762/get-application-version-name-using-adb
The best command so far is:
adb shell dumpsys package com.google.android.apps.photos | grep versionName
How to get the package name: View app's full package name?
But this method is not perfect, as they can give multiple results because of the
Hidden system packages: section.
Feature request for Google Play Store
Those would be ideal places for it: