I came across this issue if you have external Platform Service Controller/s (PSC), and then deploy a vCenter instance paired to the PSC, and you update the SSL certificates on the PSC and vCenter instances.
After rebooting the vCenter and logging in via the Web Client I was presented with a message “Error occurred while processing request. Check vSphere WebClient logs for details”. Doing some log searching and Googling I hit this VMware KB article which resolves the issue.
Follow the instructions in the KB to resolve. As we are implementing a new multi -PSC/multi-vCenter deployment I needed to do this process on the PSCs and the vCenters.
The problem as per the KB is:
Some solutions, such as VMware vCenter Site Recovery Manager, VMware vSphere Replication, or VMware vCenter Support Assistant are always installed on a different machine than the associated vCenter Server system or Platform Services Controller that manages the certificates for the solution.