At the beginning of the scene, it distinctly says in a subtitle, "Hollywood, 1944". But watch the last scene closely, after the Judge has been dipped and a bunch of cartoon characters have gathered around.

Among these characters are Sylvester, Yosemite Sam, and Road Runner. However, Sylvester and Yosemite Sam were not created until 1945, and Road Runner in 1949. Also, the dance Bugs Bunny performs when "Smile, Darn Ya, Smile" plays at the end was not created until the 1947 cartoon "Slick Hare". And in the middle of the movie, Eddie Valiant falls victim to Tweety Bird's "This Widdle Piddy" gag. But Tweety is yellow, and in 1944 he wasn't drawn with feathers yet. He should have been pink.(But then again, can you blame Disney for totally screwing up the Looney Tunes?)