Fix in short: switch Google Play to a different Google Account, and switch back to the original account. It can be a new Google account, or one that already exists on your phone.
I hope that helps, and if you want screenshots & more details, read on.
(Short version because, apparently, this post is #3 on Google for “Google Play RPC:S-5”, and variations thereof, and putting the fix in the description that Google will show seems like a Good Thing to Do.)
If you’re unlucky, like me, you’re getting an error like this when you try to update stuff on your shiny Android
4.1(.1) device: (Edit: Apparently, not just Android 4.1.1, I’ve seen reports of 4.2 breaking too.)
The most common ‘solution’ I’ve seen is to completely remove your Google account, and re-add it.
Which seemed a bit extreme, given that it’d (supposedly) wipe all your stuff off the phone. A solution that I stumbled upon is to simply switch to a different Google account in Google Play (Tap the options button at the top right), install an update, then switch back to your original account, and install the rest of the updates.
That got it working for me. It’s possible that you don’t even need to install an app in the other account – just switching back and forth might be enough to get Google Play to update whatever cached file is breaking. (I’m assuming it’s a cached file, that is.)
Apparently, this is an unexpected result of flushing and restarting the Google Services Framework in an attempt to force Android to detect/receive the update to Android 4.2. (Which, sadly, didn’t work for me, possibly because I’m on Wind in Canada. Oh well.)