The errors you posted were from the client. Assuming you can ssh into the remote machine without a problem, do you see error messages there on the server?
Thanks, Akemi, you have hit the nail on the head!
The spurious error message was caused by a statement in .cshrc that created output, a stray unescaped exclamation mark in an alias definition. And that with me preaching to my users for years about cleaning up their init files ...
I feel stupid now. But not contagious, thankfully.