After actually seeing it live:
The greeting is weird and a waste of space, at least make it a dismissible banner and ideally only if someone hasn't been seen for a while, though that might be even more annoying when it does pop up.
The widgets are nothing but an even more annoying waste of space that belong in the profile—where they already are and have been since their introduction—and at the least should be configurable (show/hide, type, order).
The "personalized" list doesn't have any more relevance to me than the /questions list. It seems like it's even less relevant, but I think that's just because it doesn't even distinguish favorite tags. WTF is that?
When I go to the homepage, I want to see the questions with the most recent activity, just like it always has been. That, btw, is going to be much more important on other, smaller sites that rely on a handful of active users keeping an eye on everything.
It's so annoying to keep having to go back and add /questions, I'm going to make sure to dedicate some more time to the iOS client I've been poking at here and there.
After mulling things over for a bit I think I'd summarize this update as forcing a pushy new-and-returning-user experience on the site's oldest and most active members every single time we come here. You're targeting the wrong people. And over the years, I've seen the company's receptivity to feedback wax and wane, but I've gotta say this redesign certainly seems like a new low for willingness to listen to your users.