It is rather silly to apology on behalf of America. It is like the Pope of Roman Catholic apologizing for all Christians on what he personally feels are faults or failings, that may or may not have happened in that or other particular denomination; I find it ignorant speaking for other people on what individual principles you may so follow.
He is a person, in the most simple form, who will only serve for eights as commander-and-chief, but a single citizen, nonetheless. Once he is a former-president I do not believe he will enjoy having the next president apologize for him simple because the current president personally felt Obama was wrong.
Whether or not of there being any wrongs, faults, or failings, it is still someone selectively airing a personal opinion of a very large and complex issue on behalf of everyone with no regard to them.
He should not have apologized for our belief in free speech. That is a fundamental part of our government, of what our country was founded on. He should have condemned the stupidity and intolerance of the guy who made the stupid movie, should have called him out as disrespectful and childish, but acknowledged that he was within his rights.
President Obama is the leader of our country, what he says and does, or does not say or do reflects on our country, good and bad. It's better to apologize for those few who choose to act out against other countries and religions and to let them know that we as a country do not agree with it.
The radical Islamists have an ideology that insists that half the population not participate in commerce and public life; an ideology that sees Israel as the focus of evil in this world to be incinerated and its ashen remnants pushed into the sea; an ideology that shuns science and innovation for a return to the seventh century; an ideology that denies individual freedom and economic freedom alike; an ideology that revels in a cult of death and martyrdom; an ideology that denies the very existence of the nation state; an ideology that seeks retribution for supposed wrongs inflicted in past centuries instead of working to build a better future.
Obama wasn't wrong to apologize for America. We have a lot to be sorry for. Republicans tried to impeach a president for having an illicit affair. A filmmaker made a so-called "movie" that disparaged Muslims. We idolize Britney Spears, reality TV and eat mega-buffets. Imagine if we took our TV time and reached out to help our fellow humans instead? Americans are a sorry bunch.
If Obama had been actually "apologizing for America," then I would take issue with it. However, he did not go so far. He was condemning a certain offensive film and saying that the rest of America didn't necessarily feel that way. Those are both valid things to say. He also said that Americans condemned a violent retort to that film.