Since a while I enabled a semi-automated reporting of a very heavily used script on WikimediCommons.
The user has the possibility to press a button to post the error message to a list of those.
Now, after about 1 month there are 4 reported (this means that this occurs much more often) errors:
API request returned code 200 parsererror. Error code is SyntaxError: JSON.parse: Parsed string contains more than single value: <!DOCTY...
API request returned code 200 parsererror. Error code is SyntaxError: JSON.parse: unexpected non-whitespace character after JSON data
This means that jQuery received a 200 response and tried to build a JS-object for the presumed json-string and that failed.
Since we are using "secure techniques" (js objects) to build the query string, and the format-parameter is always set to json by a wrapper-method (all requests are handled by doAPICall), this problem only occurs when editing, I think the problem is at the server side.
If you would like to be up-to-date with those issues, just watch https://secure.wikimedia.org/wikipedia/commons/wiki/MediaWiki_talk:AjaxQuickDelete.js/auto-errors for new entries with "API request returned code" (I could make a separate page for server errors, if you want or send them with JSONP to a health-status-server.
It's a page you can learn a lot from: E.g. "API request failed (hookaborted): The modification you tried to make was aborted by an extension hook" is a very bad error-message. User has to guess which hook of the the thousands.)