vSphere Client could not connect to "vcenter.mydomain.local". The server could not interpret the communication from the client. (The remote server returned
an error: (503) Server Unavailable.)
So you're happily working away one day then all of a sudden you get an error when you attempt to connect to vCenter using your trusty vsphere client (because youd rather gnaw your own arm off than use the web client). But why the error when nothing has really changed on the vcenter side of the things and youre vsphere client has been the same for years!
Just relax, your vCenter hasnt exploded and you wont be working until 3am tonight ;) Hopefully this could be a simple proxy issue, if youre using one that is. If you are, then simply add your vcenter's fully qualified domain name to your internet explorer proxy exceptions list and try again.
Open Internet explorer optons -> Connections tab -> LAN Settings as shown below. Click inside the exceptions text box and vCenter address to list. Click OK and then try reconnecting to vCenter again. With any luck thats all it was and you can breath easy ;) Happy clicking!