So far I see ONE American in this thread who gives the correct reason why bowing to a monarch should not be done.
#1 The emperor of Japan is a ceremonial figure only.
#2 The government of Japan is elected.
Bowing to the emperor of Japan is acknowledging that you honor their beliefs and their traditions. If you do it correctly. In Japan, the emperor is considered (or was... culture is changing slowly) a deity. A god.
Obama's bow was a show of respect. Nothing more. Japanese are not stupid, anymore than Americans are (however, if some of the people in this thread are representative of Americans, I'm getting really worried about our country and the sheer amount of ignorance and inferiority they've managed to develop. It takes hard work to look as stupid as some of the folks here...).
Japanese that saw that bow recognize why it was made and how it was meant. It's no different than a foreign dignitary attempting to shake hands and screwing it up. People reading any more into it than that either are total fools are have ulterior motives for wanting to believe Obama 'screwed up'.
PS. I'm conservative, and don't care for Obama, but the right-wingers here are making total fools of themselves harping on this non-issue.