I know that doorway pages are bad, but my partner hired an SEO firm years ago who recommended doorway pages. We just moved our site to a new domain and in the process I deleted all of the doorway pages. However, it appears that some pages might still be linking to them since the googlebot is trying to index those pages. Since the pages don't exist it is returning a 404 error, however the pages appear in the google index when I do a search on site:mydomain.com. These pages have no title or description.
My question is will these non-existing doorway pages hurt us in the Google rankings? Is it normal for Google to index pages that return a 404?
Thanks for your help.