1. Log out and look at the homepage on a phone or screen smaller than 640px wide
2. Notice the grey box and the Tweets section are closer to the right of the screen than the left, and the News and Find you favorites sections are slightly closer to the left than the right
They should all be centered.
Testing notes: Following the great unsquishing in AO3-4291, assuming your default font size is 16px, this can be tested in windows starting at 672px wide rather than 640px.
Two related issues cropped up while working on this, so please also check
1. That the title/date/comments section of news items on the logged-in mobile homepage is now correctly aligned above the left edge of the news post text
2. That the OTW Tweets box is now centered under the tweets heading, logged in or out (this will be easier to check on a slightly wider screen – you can't tell in portrait mode on my iPhone 6, for example, but you can tell in landscape mode, even though both trigger the narrow-width layout)
Looks good on Android S6 Chrome, and I checked logged in as well as logged out to confirm nothing broke in the process.
Looked at all the things logged in and logged out, portrait and landscape, and everything looks centered / aligned as described. (iPhone 6S, iOS 9.2)
The various bits on the homepage (news, tweets, comments, blurb, etc) look aligned in HTC One (Android 6), both in the default browser and Opera Mobile, in both portrait and landscape, logged out and in.
(Opera is trying to save data, probably, and doesn't rejiggle when first switching from portrait to landscape, but refreshing the page gives the right alignment, so I'll chalk this one up to Opera being helpy.)
Things look centered in the narrowest squish window in Safari, Firefox and Chrome on the Mac, and with the stock browser in Android 4.1.2 (Samsung Galaxy S2).