I resist commenting on the bow because, well even commenting on it seems to elevate the idiots who complain about it.
The larger point has yet to be made so a broader view may be helpful.
The President's bow wasn't a mistake or a misstep.
It is part of his charm offense. He is trying to win the ordinary citizen of other countries back to having warm feelings for the United States.
He makes the bow in Saudia Arabia and Japan, where culture considers public respect just good manners, unambiguous.
He has town hall meetings. He answers questions from ordinary citizens and students. He even tries a few words in the local language.
It is a world wide charm offensive aimed at giving people the message over and over again that the United States is much larger than the Bush/Cheney folks that seemed to confirm the type of superficial jingoistic images that they often see in movies.
If you are an American living overseas in a country that is not proficient in English and you are able to converse in the local language you will find ordinary people jump at the chance to connect with you simply because you are from the US.
Usually it starts with a confirmation that you are in fact American. Once that is established an attempt will be made to find someother more personal connection. Here is one that I remember from 1977:
Foriegner: "Where in the US are you from?
Me: "Washington State"
Foriegner: "Oh then you probably know my cousin - he lives in Florida, his name is 'tiny'".
Me: "No sorry I don't know 'tiny' who lives in Florida".
Foreigner: "My teacher went to Ohio State University - surely you have been there, he said it is the biggest and best University in America."
Me: "I have never had the privledge of visiting Ohio State but I have seen its football team play on TV".
Foreigner: (Somewhat disappointed at not having made a connection with either cousin 'tiny' or something more intimate than watching USC pummel OSU in football he thinks for a minute)
"President John F Kennedy came here in 1962. He met with our King and he greeted us in Thai. President Kennedy is a very great man."
Fifteen years later this guy remembered the President's visit as if JFK stopped by and had dinner with him.
What was Fox and the peanut gallery complaining about 4 weeks ago? Can't remember and its not important. Watching their idiotic comments in the run up to the Iraqi War it was clear that none of these halfwits have ever lived outside the United States.
Four weeks from now no one in the United States will remember the bow, the town hall meeting or the President meeting with all of the different leaders in Asia, they will be pursuing some equally inane point.
But the average Japanese and average Asian will remember. They will remember an American leader who demonstrates respect and manners.
From their point of view President Obama wasn't bowing to an Emperor, he was bowing to them.