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John Mueller of Google said this morning in a hangout on YouTube at the 5:40 mark into the video that moving your header tags, i.e. <h1> and/or <h2> and so on, around on the page won't make your rankings go up or down.
So if you have them out of order where H2 is first and H1 is second or if you have H3 several times on a page or if you have H1 more than once on a page - it doesn't matter.
John Mueller said "It is not the case that you’d see any ranking change by shuffling headings around on a page."
So shuffling your header tags around on the page likely won't impact your rankings in Google search.
Forum discussion at Google+.
