The Problem
I got the following error message:Update for "Foursquare" could not be downloaded due to an error. (Error retrieving information from server. [RPC:AEC:0])
This would apply to any app, but for my case both Foursquare and Google Music.
I tried a lot of different things from clearing the cache of each of these apps as well as the Google Play app, to even uninstalling the Foursquare app and re-downloading it. None of which worked.
Solution
In the end, I found this link which pointed me in the right direction.The workaround is to simply to go to Settings->Accounts&Sync->Google and removing my Google account. Afterwards, just add it back again. Then the error message disappeared and I could update/install apps once again.