Ok, I have to defend the guy.
1. He was great in Howl!
2. I just read this article, which somebody posted above. To clear things up a bit, the article says he'll be pursuing a doctorate in English & Film Studies. This doesn't mean he's running off to another program as many of us assumed--since I'm currently applying to the same program, allow me to explain: When you apply to Film Studies at Yale, you have to choose a second department from which you will receive a joint Ph.D. I am applying to Film & Art History, but given his academic background, it makes sense that he'd apply to Film & English. One generally applies through the department one is strongest in, so for him that would be English, once again given his academic background. I'm sure he was accepted because of the freshness and originality of his ideas and/or approach, not simply because he's famous. The adcoms were clearly thinking about the richness of classroom discussion and his potential contributions to the field--they have too much invested in their departments to simply let him in for fame's sake. As for the graduate school itself, they may have been willing to take slightly lower composite GRE scores in exchange for the publicity, but hey--that's the nature of graduate schools everywhere. They have to think about their numbers, their rankings, their fame, etc.
3. I've definitely fallen asleep in classes not related to my field. Didn't we all have to fulfill distribution requirements at the beginning of undergrad? I'm pretty sure my Earth & Planetary Science course was the most boring experience I've ever had. Now, it's equally possible that those photos of him were taken during his Milton class, but I've definitely taken some boring film classes before, and I have definitely fallen asleep. Nobody's perfect. And if you're like me--I worked two jobs and ran 2 clubs during undergrad, while also double-majoring--you didn't get a lot of sleep. As a result, boring, soporific lectures tended to induce accidental naptime. I wouldn't judge his ability to pursue graduate study based on these types of occurrences.
4. As others have suggested, I wouldn't be at all surprised if he's not funded. I also wouldn't be surprised if Yale told him he had to minimize or completely stop his Hollywood work during his studies, just as the rest of us have to stay out of regular jobs. He's probably finished the filming portion of everything he's been working on (Eat Pray Love, 127 Hours, The Iceman, etc.), and now he's putting acting on pause while he does his residency requirements (which I believe are 2-3 years for most programs). I wouldn't be surprised if he fudged the period of dissertation research with a little acting, but since he's paying for his own education, I don't see how it's all that bad--many people spend upwards of 10 years completing their diss, so he wouldn't be alone.
5. Even if he doesn't end up producing scholarly papers or teaching somewhere, I don't think this makes him somehow less worthy. With the job market as cutthroat as it is, I don't think we need him as a competitor, anyway. And, as I believe someone else mentioned, not everyone with Ph.D. after their name publishes or teaches all that much, and that's okay.
Alrighty, I've said my piece.