Kerry Howley dismantles it:
Here is a Sean-Hannity-endorsed highlight reel of Obama apologizing in which, you will notice, Obama never apologizes. He makes what we might call "admissions" that the government of the United States has made mistakes. What these mistakes consist of remains mysterious, because Obama declines to give the kind of specifics that would provide such an admission any rhetorical force. "The United States," he says, "is still working through some of our own darker periods in our history." This counts, in some quarters, as an apology, but it’s a statement even the people most worked up about "apologizing for America" would probably agree with, should it come from someone else. Perhaps the reel is better termed, "things Sean Hannity finds galling when they come out of Barack Obama’s mouth." I take it to be the case, in watching these clips, that it’s hard to find footage of Obama actually saying he is sorry.