Just for information: If an edit fails because of a CAPTCHA (missing or not/false solved), the API should return all relevant information:

{"edit":{"captcha":{"type":"image","mime":"image/png","id":"1610928352","url":"/index.php?title=Special:Captcha/image&wpCaptchaId=1610928352"},"result":"Failure"}}

The url parameter is the link to load the captcha image from. With the id parameter and the value of the user (who solves the CAPTCHA) you can retry the save api call with the relevant data, e.g. (for an edit):

action=edit&format=json&title=Pagetitle&summary=&captchaid=1610928352&captchaword=edvfd // and all other required parameters

Hope that helps :P

If you manage a Wikibase instance and wonder why your users can't enter email addresses or URLs while you can as admin, you have probably hit this bug.