Since a few ppl have asked, some more details on Kristen's edited interview.
There was a whole exchange in between 'I had a good birthday' and 'you just flew in from somewhere, right?'
Jay asked her what her favorite (or best) birthday was. She paused and went, hmmmmmmm. Imagine the BD First when they're asked the best gift they've received or her being asked her favorite London memory in Glamour UK. It looked like she was thinking of some answer she would never actually give (which led us to guess Budapest but she never actually said that and likely, never would.)
When she couldn't come up with anything, Jay threw out, 21? 18? She jumped on 18 and said that it was a big deal because she could work longer hours and they talked a little about child labor laws. It was cute because Jay said sth like, you can only work 4 hours or something? And Kristen, like, put on a cute little expert voice and said, well you can work 9 hours and then you must do three hours of school (or something like that). So then she said that her bday gift was a 16 hour workday (which she's said before) and that they had a cake on set but she stumbled over that bit and first said, she had a 'clock in the shape of a cake' and then adorably corrected herself to 'cake in the shape of a clock' in typical self-deprecating Stew fashion. Jay said 'cake in the shape of a clock', that'd be interesting and she said, yeah I'm trying to figure out that one too (or something very similar.)
Then they moved on to the talk about Vancouver. I tweeted last night that they cut just a little bit of that when they talked about the Renesmee dolls and Kristen said an infant with hair is a little weird and Jay said, well it's supposed to be creepy? Kristen giggled said, um not really.
I think those are the only things missing from the aired interview that we saw live. I'm assuming the show just ran long (perhaps the Cinco de Leno thing) because even with her birthday hesitation, none of it seemed unusable or anything. It was actually pretty cute and I always love hearing her talk about Twilight.
Hope this clears up some of the confusion about the aired interview vs. what we saw live. :)