Most of these answer with a status that looks fine. The API answers 200 with an "Error: …" string in place of a field, 200 with the whole list for a filter it ignored, "saved successfully" for a revision that is not live, and 207 for a form submission nobody will act on. So the first check is the same for all of them: read the whole answer, not only the status, and when the answer to a write looks wrong, read the record again before changing anything.
A POST that works from the admin and answers 403 from a script on the site is the CSRF token: see 403 on a form submission or a POST from JavaScript.