Duane Forrester of Bing spoke at the SMX West 2013 SEO Conference. He mentioned an interesting thing about how they treat H1 heading tags, especially in HTML5 documents where you are able to have multiple H1’s. I suggest that Google probably does the same thing, although Matt Cutts who was sitting there did not make any specific comment to Duane’s statements.
When you are using html5, you can have multiple H1’s on there “we simply look at the first one and say lets apply that to the SEO for the website, and the rest simply become design elements”
Therefore, I say you need to make sure that the first time you have an H1, that H1 is solely for that page, and not used as a global whole of site template.
I say Title that has the main search phrases in there as exact match as possible given the constraints of 70 characters. So some phrases become broad match.
A 155 character meta description that has the search phrases broad matched with a highly clickable sales pitch.
An H1 that has a dumbed down human readable sales pitch title - ie the phrase at the front of the title and say the brandname.
Then an intro paragraph that includes as exact match, the main search phrases in the title. Then include alternate search phrases scattered through the page content. The phrases are exact match of the phrases in the title, and exact match of phrases that have been broad matched in the title.
Simple stuff, but I find people so often don’t get it right.
So with each part, work hard at getting the basics right. Yes, for all its simplicity, an H1 is an important part of the SEO of a page.