When Renee Zellwegger arrives in New York, she exits her cab in front of the United Nations. The Canadian flag is visible. The movie is set in 1962, and the form of Canadian Flag in the shot was not adopted until 1965.
The ending song scene, during the credits - singing wasn't strange to either of the actors: Zellwegger had a leading role in Chicago, and McGregor in Moulin Rouge, movies where they had several song scenes. In fact, the scene was only added at the insistence of the actors.