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It's not necessarily an SEO problem (as long as you don't redirect all 404s to your homepage at least. I've seen that be an issue in the past.) However, use it as an opportunity.  Make the 404 a sales page if you have that many.  It's a lander now for "the product you were searching for is out of stock - here are the search results on our site for similar products" etc.  You can turn it into something productive to have that many 404s. From WMT, mark them as fixed and then anytime one pops up, find out what is linking to the product and try to remove that link.  You don't want to be linking to 404s internally if you can help it (bad user experience = Google's nightmare) so having 1000s of 404s isn't bad but try to break any internal links to them.  (Xenu can help as well if you don't feel like waiting for WMT.)

I have a suggestion, but please do your own research to verify this... My understanding is that you can set up a block of text on your site that is not visible until a visitor does something like clicks a tab or does a mouseover, and if you use the CSS command display:none; to make it invisible, that text will not be read by the major search  engines. That text can get displayed when the visitor clicks the tab or does a mouseover by having the CSS command switch to display:block; (or some other version of display). I think this is because a spider can't activate the tab or mouseover function. I've read this a few places and avoid doing display:none; on valuable content for this reason (better safe than sorry). But I have not read about someone using it to purposely hide content to prevent duplication issues or dilution of keyword density. It could verified with a pretty easy test. Just add some gibberish content to an existing page,  but hide it using display:none;  Then use GWT to ask for a recrawl, wait a few days, and do a search for the gibberish content. If it doesn't show up in the results, that is a good sign it worked. Let us know if you test it....