I can't answer what all the error messages would be and it might depend on which methods you are using. I check if the server is reachable, if a post for a new score was successful (return code of 201 or 202 maybe - not sure which), and for an error message containing the word profane (return code 403 is what is returned) so I can tell the player they can't use a username with a bad word in it). But, in looking through Daniel's client side code, the StatusCode.cs file contains a bunch of return codes and you might be able to check for these. I would verify with Daniel though. You could also test some of them like a 401 maybe is a bad public key (maybe), 204 might be a submission with a required param like username missing. Here are the codes that I saw, but I have no idea which ones are returned for which methods/functions. Hope this helps some.
public enum StatusCode
{
FailedToConnect = 0,
Ok = 200,
Created = 201,
Accepted = 202,
NoContent = 204,
BadRequest = 400,
Unauthorized = 401,
Forbidden = 403,
NotFound = 404,
Conflict = 409,
TooManyRequests = 429,
InternalServerError = 500,
NotImplemented = 501,
ServiceUnavailable = 503
}