Most people here got the last scene wrong (I think)
I've been reading a bunch of threads here that say the last scene means Greta had wanted to get back together with Dave but when she hears the song being butchered she changed her mind.
That makes no sense given the evidence in the scene. The arrangement sung by Dave on stage is actually a lot more barebones than the one Greta had heard before, which means he had listened to her advice and did the song more like a ballad. She didn't want to go at first because seeing him still cause her pain, but she went anyway.
When she saw him performing, she smiled because 1) she could see that he's really successful and he's happy for him and 2) she realized she didn't love him anymore and she's okay with that. This allows her to truly "begin again." This is what the last scene mean IMO.