First of all, the default title that you have at
System > Configuration > Design > Html Head > Default Title has nothing to with this error. This is because this section actually used to set different default/store-level parameters of head section of Magento. ie those items are comes inside
<head /> tag. Those values are important to set for SEO and hence should not be removed.
As per best SEO practices, you need and h1 tag in a page which clearly gives a clear hint of that page. For a category page, it should be the category name. There should be only one h1 tag present. Hence all other h1 tags in your category pages should be removed or converted to h2 tag or any other.
Multiple h1 tag error actually comes inside the content section. So you should look into the
<body /> part of your category page. In order to trace those h1 tags, you need to inspect the page source code and find h1 tag occurrences. Then find the template that inserts those duplicate h1 elements and then do work-around.
I know my answer is not specific so does your question is. This is the best we can provide for this answer. :-)