If you turn on debugging mode, it should send you the complete request/response to the 3rdparty service. The presence of "error messages" is limited to what the 3rdparty provides -- in many cases you're actually spoofing one of their provided forms (e.g. Bronto provides a webform you would normally paste on your site, but instead you map the fieldnames to CF7 fields with this plugin and submit to their form URL) and the only way to check for errors is to parse the HTML page returned by the original form you're mapping to. If you're lucky, the 3rdparty provides an API with an actual structured response you can parse.
The plugin just has a very basic "check for success" clause, since it's easier to just search the response for a success message (which would appear in a regular HTML page or a serialized response). Since the return formats vary between service, I only provided some very basic hook examples, but if you know the format of the response you could build a hook to validate.
That being said, the only "real" error I can generically handle is an actual failure to submit, which returns a WP_Error with a message I can report on -- the plugin then forces the CF7 form submission to report a failed submit, so that it shows an error message to the user on the frontend and emails the administrator.
In your case, I'd need to know the response before I could make any suggestions. If it helps, there is a screenshot of a working Salesforce integration on this plugin documentation -- does your mapping look anything like it?