AND notice how the people in the Chan films who mock him and make racist comments toward him are portrayed as the ignorant ones, as he ultimately proves by way of his own patience and intelligence. I watched Charlie Chan in Paris recently, and the guy who makes fun of his accent is clearly supposed to be a jack-ass.
As for Number One Son, I can remember at least one -- Charlie Chan in Rio -- where a white woman talks about how he is cute and wants to get with him, and this is actually shown in a positive light. This seems like a big deal to me, although it is never mentioned. All of the sons and daughters speak like first-generation Americans, and the reason they are less patient or intelligent is because they are Americanized (although there are rare occasions when one of the sons actually figures something out and helps with a clue). I think there is a lot of truth in this and have never viewed the sons or Number One Daughter as being particularly negative.