Bing flags multiple H1's as an issue of high importance--any case studies?

[nicole.healthline]

Going through Bing's SEO Analyzer and found that Bing thinks having multiple H1's on a page is an issue.

It's going to be quite a bit of work to remove the H1 tags from various pages. Do you think this is a major issue or not? Does anyone know of any case studies / interviews to show that fixing this will lead to improvement?

[kadesmith]

I don't know of any case studies, but I remembered reading a couple posts about H1's a couple months back: http://www.seomoz.org/q/multiple-h1-tags-on-same-page

and another from earlier in the year: http://www.seomoz.org/q/one-h1-tag-dead-long-live-multiple-h1-tags