From a technical point of view this "redesign" scares me a bit: All the old stories and user accounts 404 now. That is a major loss to their SEO. 14 million pages just thrown away and not passing any juice. They don't employ canonical or robots.txt. They have character encoding issues. ("'Superbird' Discovered") They use a meta keywords tag, and it contains "celebrity news", which doesn't appear anywhere on their sit…
Apart from all the old pages being 404 (which is a huge mishap). Nitpicking on html is a fun and amusing pastime, but unless the page is deformed in some way, it falls into the "shit nobody cares about" category.
But if you care about accessibility, usability and SEO you should probably care about HTML issues like pagespeed and validation.
Web Content Accessibility Guidelines 1.0
Create documents that validate to published formal
grammars.
http://www.useit.com/alertbox/response-times.html
Users still hate slow sites and don't hesitate telling us.
Google Webmaster Guidelines (Design & Content)
Check for broken links and correct HTML.
So perhaps it is the "shit nobody, but front-end engineers, should care about" category.