Similar issue with OWA now broken. Environment: Exchange 2013 on Windows Server 2012, Full-Hybrid, latest updates. I saw the reports in the comments about OWA redirect for hybrid not working so I tested it before I ran the updates and all was well. Updated the cluster and now it no longer works. Error displayed: External component has thrown an exception.
I ran through the scenarios linked at the top of this article to repair failed installations of Exchange and nothing applies and anything to do with OWA/ECP checks out. ECP works just fine. Installed through Windows update after shutting down all Exchange services and WMI. Install was successful with no errors and everything else is working as expected.