Question: How does a movie like Extremely Loud & Incredibly Close not manage to even get above 50% on Rotten Tomatoes, but still gets a nod for best picture? Do we just need Tom Hanks and 9/11 in a movie and that is good enough?

Pretty much.  Its just like Midnight In Paris.  I mean, I love Woody and all but this film doesn’t scream BEST PICTURE at all.  Its not Annie Hall by any means, why would they do this?  I would take a guess and say, hes a big name and we needed a one more film, 8 best picture nods would have just been ridiculous.  Also, check this from wiki

Despite friendly recognition from the Academy, Allen has consistently refused to attend the ceremony or acknowledge his Oscar wins. He broke this pattern only once. At the Academy Awards ceremony in 2002, Allen made an unannounced appearance, making a plea for producers to continue filming their movies in New York City after the 9–11 attacks, where he stated, “I didn’t have to present anything. I didn’t have to accept anything. I just had to talk about New York City.”^[61] He was given a standing ovation before introducing a montage of movie clips featuring New York.