An Android app I needed to use refused to allow me into it unless I updated it.

BONUS: Every time I hit the update button, it took me to the iTunes Store.

So, I went to the Google Play Store. It said I had the current version. So, I visited the store from a laptop computer which said I was two minor versions behind. (2.0.9 was current and I had 2.0.7.)

I tried re-installing the app. It installed 2.0.7 again.

I tried the nuclear option deleting the cache & data and then restarting the phone. When it came back, it recognized that it needed an update.

In retrospect, maybe the Google Play app needed to be the one I deleted the cache for? It seems the problem was it not getting the new information about apps.