Just before the plane from Hawai'i to San Francisco lands, Chan and the other passengers are told they have to go through customs. Though not yet a state, Hawai'i was already under U.S. jurisdiction and therefore passengers flying from there to the U.S. mainland would not have had to go through customs.
As Chan's airplane approaches San Francisco, we briefly see a stock shot of the uncompleted eastern span of the Bay Bridge. The bridge opened more than two years before the Golden Gate International Exposition, the film's setting.
When Charlie returns to Dr Zodiac's house (at 1:14hr), the scared taxi driver refuses to wait but he doesn't grab hold of the money properly so when he tries to take it, the notes slip though his fingers.