In traditional media, trust in news was established by ethical behavior, like good intent backed up by checking the facts.
Distrust in the press grows when traditional journalistic values, like fact-checking, are forgotten.
Fact-checking is a lot of work and frequently expensive, and in today's media environment, there are a few cases where it's done in good faith as it is at The New Yorker and Consumer Reports.
For a while, two groups which have done really good work trying to restore this tradition, are FactCheck.org and also PolitiFact.com. Even when I disagree, usually regarding excessive literalism, I see they're doing good work. (As a nerd, I should be the excessively literal one.)
Recently, a genuinely big deal traditional journalism guy, Jay Rosen, suggested that the Sunday morning political talk shows start fact-checking their guests, big politicians. This sounds great; I talk to a lot of reporters who are frustrated when they know their guests aren't being honest.
Jake Tapper, on This Week on ABC, has taken up the gauntlet, and engaged PolitiFact to do the right thing, with promising results. I'm impressed, and now take the show seriously.
On the other hand, the folks at Meet the Press have the opposite take, and prefer to enable career politicians to get away with all kinds of stuff. A group called MeetTheFacts.com is trying to convince them to do the right thing, even adding a Facebook fan page.
MediaBugs.org from Scott Rosenberg also looks pretty good
This is a promising trend, and I feel that it's a survival strategy for news media. Trust is required to survive. There's a window of opportunity now for restoring trust, but it won't last forever. The winners will be serious about fact checking.
Disclaimer: because of their really good work, I'm involved with both Consumer Reports and also with FactCheck.org
More specifically, I'm on the board of Consumer Reports (Consumers Union) and on the advisory board of FactCheckED.org, which is their education arm.