Thinking of fixing the multiple H1 tags in your HTML5 site? Wait… read this before doing a fix.
It has been somewhat a cardinal rule in pre-HTML5 that every page should only have 1 H1 tag for 2 reasons: 1) to ensure that search engines can properly index the page, and 2) to ensure that the markup is according to W3C standard. With HTML5, it is not just possible to have these multiple H1 tags, it is in most cases the recommened course as Kezz Bracey explained at The Truth About Multiple H1 Tags in the HTML5 Era. The sectioning elements in HTML5 makes it possible for an H1 tag to be used for each section of a page. This is typical for HTML5 blogs.
If you still wonder what Google thinks, here is something from them in the person of Matt Cutts:
Whether or not you stick to the single h1 tag when using HTML5 is up to you. The question to really ask would be: are you delivering quality content to your readers?