Not sure this is the correct forum section. I just checked Bing Webmaster Tools and for a site they used to have positioned 2-3rd they now say that having 6 H1 tags is wrong and the page should only have 1 - for SEO purposes.
On most pages I have 4-6 <h1> tags for titles and had never considered that having more than one could end up being penalised in a search engine.
Is this just Bing being Bing or is there a serious issue in only using one H1 tag per page?
Judging from your description of the message in Bing Webmaster Tools, you're not being penalized for this. Rather, you are given a tip on improving the validity (or helpfulness) of your HTML. Having multiple H1 elements is, indeed, wrong, and makes it more difficult for any search engine to determine what the page is about.