The question came up in today’s Google webmaster workplace hours with John Mueller regarding whether or not there are any ranking problems with pages that utilize h tags in such some way that the tag won't precede other tags.
Here is what John said:
"It doesn’t really matter. We use the headings to understand the context of the content on the page a little bit better and for that, we don’t need like a strict order of the heading tags.
Sometimes you have multiple h1, sometimes you have, I don’t know, the order is slightly different because of your template or something on your page and that’s perfectly fine."
So if you've got misordered H tags on a page, there's no real reason to form any changes, as long as you make sure the most vital header is residing among the H1 tags on the page.
