In my opinion, journalism's responsibility to the public is, first and foremost, not to be sloppy. There is no reason why Adam Lanza's brother should have been initially reported as the shooter. There's no reason why guns should have been reported as being used that were actually located in Lanza's trunk. The media needs to do their research.
On the same thought process, my parents were in an accident a few years ago when a deer ran in front of a motorcycle. Three different newspapers and one online documentation reported the story entirely differently. One article said that they were going 40 miles an hour down the highway. Another said that they were going 55. Additionally, two different highways were reported as the scene of the accident in two different sources. And, in one article, my parents had been released from the hospital and in another, my dad was in critical condition.
All of these differences were reported in four stories that were only one small paragraph long. In reality, my parents were going 50 mph down Highway 68 when a deer ran in front of them. Although my mother was severely traumatized and my dad injured his knee and finger, neither were in critical condition. My mother was released that night and my dad stayed over night, but only so the hospital could administer strong pain medication.
What happened? The story was so simple-- all they needed was a police report. If the media struggles so much with a simple story, how can we trust them to report the big things?
I say all of this to make the point that, in my opinion, the media's responsibility to the public is to get the story right, the first time. Journalism is these people's occupation. Other bosses in other fields would never accept such sloppy work.