I've been using the web API sucesfully but I got stumped on CORS problems with POST request. I changed the authentication method but I only made GET request impossible. GET request fail with a 401 error code, which make even basic browsing of the web API impossible since the only thing that is displayed is "Message": "Authorization has been denied for this request.". The API documentation also badly load so it may be a problem with the API itself.
According to the console log, it fails to load the js script so not even the API seems to be able to access itself. Here's a screenshot of my setting. I only have "Anonymous" in my authentication setting.