Questions
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Why might Google be crawling via old sitemap, when the new one has been submitted and verified?
Yes it should. However, as Alan mentioned below, if you still have links pointing to the 404 pages, Google will always attempt to crawl them, and will keep you informed that you have errors. If you do have external links to those 404 pages, you can 301 redirect them to an appropriate page using .htaccess. This way you'll keep the link value and also get rid of the Webmaster Tools error. If you don't have any links to them, then yes, Google will eventually stop trying to crawl them.
Moz Tools | | mihaiaperghis0