1. Everyone bows in Japan, regardless of their position. It's culturally appropriate. Although Japanese will shake hands, bowing is the culturally traditional gesture. (Obama's combined bow and hand shaking, together, was awkward and not technically correct, but he should get a B for effort...)
2. Obama was on a mission to mend recently damaged relations with Japan. But in the model of George W. Bush's diplomacy, if a president shows any gesture of kindness or decorum, it makes the U.S. look weak.
3. Just because someone bows to another person, it does not mean that one person is inferior to another. This is how bowing is different in the west from the east.
4. George W. Bush bowed to the pope, and Nixon bowed to Akihito's father, Hirohito, a Japanese emperor with a far-more troubled past:
5. As anyone who has lived in or traveled to Japan knows, Japanese culture is complicated and full of protocol, and every foreigner makes constant faux pas. The emperor's smile probably indicated his appreciation of the president's gesture, combined with amusement at how he flubbed up the bow.
I'd rather have a president who is a diplomat and makes efforts to be culturally appropriate (although he could have received better coaching from the State Department!) than one who is a macho bully and makes enemies abroad.