I have an non-productive server (914609) where the vSphere Clients (78xxxx) runs without any problem.
Just to be sure I followed your instructions (also André Pett) and upgraded to the new vSphere Client 941893. It works with the non-productive, but does not work (as expected) with the productive server. Same Error message as mentioned in another posting.
Nevertheless your concern about the client version was right: A 5.0 vSphere Client connecting to a 5.1 Host would bring the same error message.
And unfortunately I do not have VC nor can I view any files on the host, because SSH-TSM is disabled.