We are a premium theme developer and this feature is generating needless threads and messages on our support forum and via private messages, as individuals think your new methods which produce the warnings are theme core code errors, not content errors.
As BackuPs above has requested, please provide a method, preferably a setting, that allows the page check to be turned off.
It seems that what you have done is created the page check feature, and if the site designer does not follow your rules, then they get errors on the page check. Due to the language you use, such as "No heading tags appear in the copy" for reporting your page check opinion that the page is not fully optimized, users are getting confused. We know that Copy = Content, but others might not. So you perhaps also need to examine your use of nomenclature, as the strictest use may not be the popular use.
In any case, while we have always strongly recommended your plugin to our premium theme user base (in excess of 11000 users for our theme) changes such as this would start to make it more difficult to recommend, as you have not provided users the option of opting out of the feature.
It is important to remember that while you (and we) may have opinions on what constitutes proper SEO for a page, post, site, etc, others may not share that opinion, or may have alternative or concurrent methods for SEO.
So please make this feature switchable.