- First he was criticized for bowing to Saudi King Abdullah  (representing Americas deference to Oil and Islam), an insult to both.
- Then he acted shocked when his opposition complained.
- Then he denied he did it (claiming it wasn't a bow), then tried to justify it (it was just showing respect). So they yelled louder to try to teach him manners are important.
- He ignored them and went on to repeat the bad etiquette and bowed to the emperor of Japan, inappropriately. 
- Not only was he wrong to do it, but he didn't even know how to do it correctly; leaders nod-bow, not bend at the waist, and you never do it while making contact (like shaking a hand).
- This embarrassed Japanese so much, that most local papers didn't show the picture that was infamous in the west, because it showed him (and their ally: America) in a bad light.
Did he learn? No.
He went on to bow 6 more times to other leaders , proving, he's incapable of growth.
Is this a huge deal? Probably not. Our allies can get over it, and other than being mocked for being ugly Americans farting at the dinner table, this isn't likely to have huge ramifications. But the Press had a field day when GWB once squeezed the neck of a friend (Angela Merkel) at a dinner, as over-the-rop tacky (and it was front page news and lead many reports), and Obama's gaff was orders of magnitude worse than that... and not a one-off event. They attack Trump or Reagan for far less. So the point isn't that I think Obama irreparably harmed the U.S. by showing how culturally ignorant he is, to me it's about the double-standard or deniers that pretend Obama was smooth and couth because their partisan media outlets glossed over the rough edges for them.
- Obama bows to Saudi King Abdullah : http://www.washingtontimes.com/news/2009/apr/07/barack-takes-a-bow/
- Obama bows to Japese emperor, and does it wrong: http://www.telegraph.co.uk/news/worldnews/barackobama/6580190/Barack-Obama-criticised-for-treasonous-bow-to-Japanese-emperor.html
- Obama bows 8 times total: http://www.whitehousedossier.com/2012/06/20/obama-bowed-eight-times-president/