I think the first, and probably the foremost, would have to be trust. How much trust can you place in the information given to you by a source? And since every story, no matter how big or how small is derived from various sources of even more varying credibility, how much can a reporter, a newspaper, or a media outlet put into corroborating information?
It's a question I can't answer.
Though I do believe the New York Times did the best it could with what it had. While the old standard of American journalism may have become tarnished in recent years, this isn't a case of sensationalization or a false report (*cough* Jason Blair *cough*), but a story that editors evaluated fully.
The Times did the right thing by saying "hey, we didn't get this completely wrong, but we didn't get it all right either. And for that we apologize."
In a situation where editors could have easily made a number of excuses for the problems with the mother's account of her tribulations, approaching deadlines, corroborating evidence, the credibility of the photojournalist, etc., they took the higher road. In a time where every mistake, every missed fact, every poorly chosen adjective chips away a little bit more at the public trust of newspapers, editors, reporters and photographers alike, the Times may have made a step in the right direction.
