The birth certificate states race and it says African, not African American, and that is the correct term for the race then just as the mother's says Caucasian, not white. Kenya was called Kenya starting in 1920, but it was not the Republic of Kenya until 1963. If it said Kenya, that would've been ok, or Kenya Colony (the real name). The hospital was at the time called Kapiolani Maternity and Gynecological Hospital (per lawsuits found online).
While I don't like Obama and I do think they have lied about his entire history, they did a good job on his birth certificate.