The original movie The Green Hornet is mentioned in the movie, while it is part of the homage to Bruce Lee, the movie came out in 1940, 15 years after the movie takes place.
The movie is set in 1925, most of the cars are from late 1940s to early 1950s.
The motorcycle is a Chinese made Chang Jiang which is a copy of a pre-WWII German BMW. This particular motorcycle had directional lights which war era bikes did not have and was manufactured in the mid to late 1990s.
The cinema near the Casablanca is showing Bordertown (1935) with Paul Muni and Bette Davis, which would not be made for another ten years. Another poster in the same place seems to be showing Berkeley Square (1933), which is another anachronism.