Yeah, I noticed the phonograph gaffe, but I missed the "Sing, Sing, Sing" thing---shame on me! BTW, did anybody else notice the theft (ahem, "borrowing"), toward the end of the movie, of Bernard Herrmann's music from Alfred Hitchcock's "North by Northwest" (1959)? This one hit me like the proverbial "ton of bricks." Of course, there was no mention of BH in the end credits (at least, I didn't see any).
I'll see if I can dig around and find a link to the Herrmann theme, and will post it if successful.
OK, found it: the first cut on this list, at
http://www.moviemusicnow.com/play/north-by-northwest. First comes the oboe with a version of the melody, then it's restated by the clarinet solo in the form that is used in "The Artist."
Herrmann probably derived the above theme from this one in his score to "Vertigo" (1958), where it's also the love theme: first cut on this page:
http://www.moviemusicnow.com/play/vertigo
Earlier in the film there is music that's faintly reminiscent of, and surely indebted to, certain parts of Stravinsky's "Firebird" music. Well, hey, if you're gonna steal something, at least take it from the best!