The film should have ended on this scene...
It should have ended on the scene in New York with Charlie singing "Being Alive." I thought it was the perfect juxtaposition with the previous scene of the party in L.A., and would have left the viewer with just enough information to make up the rest of the story themselves without feeling like an unsatisfactory ending.
All of the expository stuff in L.A. after that added nothing and just dragged the film down, in my opinion. The purpose of those scenes seemed only to cast both of the main characters in a better light ("see, they are not such bad people after all"), but that in turn took the punch out of the film.
Also, just to add, watching that scene again, done in one long take with Driver singing for real puts me over the top in thinking that Driver should have won best actor. He carries this film.