Apparently during her first press conference - for a movie with Kim Basinger - she was asked why Kim wasn't there. She jokingly replied that Kim was dead. She describes a few seconds while the answer was translated and then she suddenly gets whipped off the stage and into media training.
Her interview with Stephen Colbert when promoting Joy, started with Colbert mistakenly saying "you play a guy in this".
Colbert: Now you play Joy Mangano, who invented the Miracle Mop. Jennifer:Yes, he did.
She also said she's been told only by her boyfriends that she aggressively slips back into a Kentucky accent when she's angry.
There's also a moment of Digging Yourself Deeper where they joke that she's not afraid to seem like she's not perfect. Jennifer says she doesn't have a choice, and Stephen implies it's because her publicist isn't doing a good enough job. He changes the subject to her parents being backstage, Jennifer explaining that their flight was delayed - and then hurriedly saying she would have brought them anyway.
Stephen: We've been here only forty-five seconds and I feel I've done nothing but attack you. Jennifer: I know, right. My whole life is destroyed. I've been dropped by my publicist, my parents are gonna be gone by the time I get backstage.
When asked if she would prefer the power of invisibility or flying, she picks invisibility so she can say she's flying and they wouldn't be able to tell the difference.
After getting her Oscar nomination for Silver Linings Playbook, she was at a party and an older woman came up to her and started congratulating her. Jennifer - who had a lot of champagne at this point - was convinced that this was Elizabeth Taylor. She didn't know that Liz had been dead for quite some time.
Her appearance on the Oscar edition of Between Two Ferns with Zach Galifianakis, (a talk show parody where the interviewer and the guest both deliberately say inappropriate things):