Victoria is right about your son needing to "claim" his citizenship. Just because he has a right to US citizenship it does not mean he is a US citizen. He has to back up his claim with proof first. And until he (or you) do so, he is not a citizen.
I've mentioned on the forum before that I am a BA agent working at the airport. I am friends with a few of the immigration officers there and here is what Scott, an immigration officer for 20 years has to say: You do NOT have to claim your son's US citizenship status at all. While the US does have the requirement for US citizens to travel on their US passports, this requirement is not exercised when a foreign passport holder who happens to have claims to US citizenship is entering the US as a tourist from a visa waiver country. Your son would only cause problems if he tried to enter the US for settlement on a foreign passport. To give you an example, let's say you were living in India and your son was born in India and had an Indian passport. In order to enter the US on an Indian passport, he would first have to apply for a visa. This is when it is important to recognize your son's US citizenship status. A person who has claims to US citizenship, should not be trying to obtain a visa for their Indian passport. Instead, they need to get an American passport. Hope that makes sense.
Whether or not your son, or anyone for that matter has an actual claim to citizenship is not and will not be determined at the point of entry into the US. Scott also says that the use of a foreign passport does NOT jeopardize your son's claims to US citizenship in the future. Any concerns there are from immigration cases that happened back in the 50's and earlier. The supreme court has since ruled - sometime in the '80's he believes - that US citizenship and claims of citizenship cannot be taken away from anyone. Rather, they, the individual, must renounce their claims to citizenship, or they must naturalize in a foreign country that requires them to give up their US citizenship (Mexico, for example, requires you to give up your US citizenship to be a citizen of their country).
Scott advises if you are hindered in any way at passport control, just know you are dealing with an officer who feels like lecturing someone that day. They will not prevent you from entering the US simply because they think your son ought to have a US passport. Just smile and nod through the lecture, then be on your way.
Brigette