I'm fairly sure the issue is related to the fact that I had installed Exchange server 2013 CU1 on a Windows server 2012 box, and then uninstalled it. I then installed Exchange Server 2013 SP1 after rebuilding the servers to 2012 R2.
When I try to install a Mail App I get the error "Exchange Server doesn't support the requested version.". I don't see any correlated errors in the event logs to figure out what exactly is going on. If I use the powershell commandlet get-app to see what apps are available for a user I get the same thing.
I do have Exchange Server 2010 SP3 servers in my domain that I will eventually be migrating off of. If anyone can give me some pointers of where to look for what might be broken I'd really appreciate it.