As far as I know, the US allows multiple citizenship if aquired by birth. But I'm not sure about that for I'm not an American.
The Japanese citizenship law requires you to abandon either the Japanese or the foreign nationality between the age of 20 and 22. But if you don't come up with the issue yourself probably nothing will happen as they don't search or even punish those. Did your mother apply to keep your Japanese citizenship when you were born?
In any case people with Japanese ancestors up to the 3. generation get a state of permanent residency.
Recently the LDP (Government Party) came up with a proposal to allow dual citizienship if aquired by birth (jus sanguinis). But the current proposal requires you to have lived at least 365 days in Japan until the age of 22 to limit dual citizenship for those with limited connection to Japan. Further information can be found here:
LDP panel mulls easing law on dual citizenship | The Japan Times Online
Hope I could help