You've heard about (or seen for yourself) the phenomenon known as Weird Twitter (too many NSFW for me to crawl through for an example, so here's a search that will start getting you there), but it turns out that Twitter itself flies the weird flag as well. A little over a month ago they announced they would stop supporting HTTP plaintext connections to the Twitter 1.1 API, requiring everything to use TLS/SSL. Perhaps since WordPress does not develop Twitter applications as a core part of its operations, this change didn't get filed in their bugtracker until after the switch had been flipped. Properly, WordPress devs contacted Twitter to ask about things, and a Twitter dev seemed to me to say that they would look into some sort of failover, but as of today the oEmbed provider in 3.5.2 still does not work for tweets.
The weirdness comes because Twitter keeps making changes with little regard for third party developers and even for average users. Remember when they decided to not-block accounts that you had selected for blocking? (Later reversed, yes, but still. And it's not like 75 million sites run WordPress or anything.) Inarguably, Twitter is a corporation whose primary mission as a capitalist actor is to gain money, not a public commons. But whether they call twitterers customers, clients, users, investors, or people, irritating them (us) enough makes that bottom line hurt, too.
As Arlo said, though, that's not what I came to tell you about. I'm here to tell you that we've updated Academic Commons (in part thanks to an old post at "And now it's all this") so that embedded tweet URIs are broken now, but should be fixed by midnight tonight. Let us know in the comments whether your site has broken embeds on or after 25 January 2014. WordPress has implemented a fix on their end, but we likely won't upgrade to that fixed version until the summertime, at which point we'll all join hands with WordPress and Twitter and sing a happy song.
I can't even come up with a good image for weird twitter, but maybe that's best considering many deny its existence.