Make sure you set the accept and or content type appropriately (possible source of 500 errors on parsing the request content):
client.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue("application/json"));
content.Headers.ContentType = new MediaTypeWithQualityHeaderValue("application/json");
Then you could just do:
var errorMessage = response.Content.ReadAsStringAsync().Result;
That's all on the client of course. WebApi should handle the formatting of the content appropriately based on the accept and/or content type. Curious, you might also be able to throw new HttpResponseException("Failed to find customer.", HttpStatusCode.NotFound);