What do the Japanese themselves think of the Bow?
Some flattered and of good will in return (to the USA), some embarrassed, some not wanting to talk about it, some laughing, and some of them, it going to their head (in a nationalist kind of, look-who-we-made-bow-despite-our-losing-WWII-gloating way). There is a variety of feelings and sentiment here. It is controversial, though.
When I showed the picture to my Japanese spouse, she winced in embarrassed pain.
It’s obviously not something that anyone considers to be very serious, but it does make Obama look like a complete and total rube.
Patting the Empress on the butt might have been worse, but only in a matter of degree. If he wasn’t the American President, I am sure he would be strongly discouraged from ever visiting Japan again.
I vaguely remember when some WH protocol officer allowed someone in the Reagan admin bow to a Japanese dignitary. And the media said it was wrong for a government official to bow.