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To reiterate what Dave and Karl have said, don't worry about the number of links, worry about user experience. Do you feel that the navigation and design you've opted for delivers a great user experience? As an aside, the average ecommerce website product category page has 3 links to every product; 1) product name, 2) product image, 3) call to action. It would be a poor user experience for any of those not to link to the product page.

completely agree. also a domain doesn't mean its your companies name, in many cases it can be but not always. good luck.

If you 301 redirect the old category page that had the bad backlinks, you will be indirectly pointing those bad backlinks from the old category page to the new one. If it shows as 404 in webmaster tools and you are no longer using that page, that means it is displaying the correct error. It should eventually be removed from Google's index if it is still in there or you could remove it from Google's index in WMT if you wanted to. Hope this helps. Mike

You know, I was going to mention that you could use the disavow tool if you suspected negative SEO.  My issue with this, though, is that I think that the vast majority of people who think they have been affected by negative SEO really have not. I regularly get people telling me that someone is negative SEO'ing them when really they've just picked up some of the low quality odd backlinks that most sites get. There have been many discussions about whether or not negative SEO exists.  I think that it can happen but that it doesn't happen often.  So, if you were very confident that you have been negative SEO'd then yes, this is a place to use the disavow tool too.