Hey Jeffrey,
So in general I wouldn't lose too much sleep over GWT 404 errors. No matter how many I've fixed, a few pop up that I have no idea how Google landed on them. The ones I'd worry about most are the ones that have links pointing to them, internal or external. GWT should give you the referring page so check those out and fix them.
If there are a few that keep cropping up just 301 redirect them to another page.
You should take a look at the sitemap and if there are /feed/ URLs in there, remove them and resubmit.
Hope that helps,
Jacob