I'm sure he's satisfied that Obama at least tried to be polite by bowing. As a representative of a whole country, Obama should have been better trained in greeting though, and should have known not to shake hands unless a hand was offered to him first.
But Americans should learn that such a simple show of respect goes a very very long way. If it was the other way around and it was our tradition to bow to our leaders, and if someone didn't bow to the president, it'd be a very different story.
Yes, America and Japan had a war, it's all in the past. Now we work for unity. If a bow is a step forward in peace, then for the sake of peace bow! Get over your pride, which is so ever preached as being a sin.