Client authorization is not necessary to generate User authentication. Client authorization is only necessary to make unauthenticated api requests.
You don't make a request to api.vimeo.com/oauth/authorize, you send your user there. You should create a link, and put it on a page for your user to click. They will make a GET request to that endpoint, but it should not happen through your server.
Since your client is making a request to /oauth/authorize, there is no way you can define the headers. You will need to provide an authorization header to /oauth/access_token, and this should be
Authorization : basic base64(client_id:client_secret)
We did fix a bug last night in our oauth error reporting :D. Sorry for the temporary confusion.
Without more information I can't really answer your error message. I'll add some comments, and then update this answer with more information.