Does having multiple H1s on a web page affect rankings?

Selected answers from the Dumb SEO Questions Facebook & G+ community.

• 
  Webado C Webada: Not unless they can be interpreted as spam. They have to make sense given the page structure. With HTML 5 you can have multiple H1`s, but usually for separate sections. If you`re going to mark up multiple sentences as H1 or any other header tag, that will look like spam.
• 
  Webado C Webada: Nothing special, the syntax for sections calls for an h1 header for a section. Outside of html 5 you`d have used an h2 probably. No extra boost.
• 
  Neil Cheesman: It is with HTML 5 that the option is there - AND with separate sections... what would be the benefit of using muliple ones - in hmtl 5?
• 
  Webado C Webada: Yes, just don`t expect miracles.
• 
  Neil Cheesman: Given the option... would you then say yes or no to this? "Use semantic HTML5 page and section headings throughout site?"
• 
  Neil Cheesman: It was already switched on... just thought it odd with multiple h1s
• 
  Webado C Webada: What was switched on?
• 
  Webado C Webada: Oh well that`s OK.
• 
  Neil Cheesman: having html semantic HTML5 page and section headings throughout site...
• 
  Jeremy L. Knauff: They probably would notice, but it takes the same amount of effort to do it correctly as it does to do it incorrectly. I am OCD about mine because it does indicate the structure of the data.
• 
  Neil Cheesman: I am not sure users would be bothered whether a heading was an h1 or not... it would depend on the font size...
• 
  Jeremy L. Knauff: No boost/benefit from SEO perspective, so look at it from a user perspective. Does it benefit them? You`ve got 6 levels to work with, use them logically instead of using extra h1s.
• 
  Webado C Webada: Visitors won`t notice the markup unless they are savvy enough to check for that. Don`t rely on header tags for style. Use css.
• 
  David Rosam: I always try to have just one h1. If there`s a need for more, it`s either too complex a layout or a Category page on a blog. If you don`t know what the main focus of the written content is, how is the poor reader to know? That`s very poor UX, if nothing else.
• 
  Tim Capper: No, not really. Its nice if you can get it sorted, but not a must have. I did a bit of work for a client, who has a aspx site with tons of H1`s everywhere, the logo, images, pretty much every line and even the footer. It has around 100K traffic a month and makes 2 mill a year and dominates in serps.