I've been noticing this recently myself -- I recently had a discussion with somebody quite anti-Bush who believes Bush has gotten a free pass from the press until recently. However I also recall Clinton haters who believed that Clinton got off too lightly. More generally, the shouts about a "liberal media" or a "corporate controlled media" show a perception that any evidence we don't like disturbs us and tends to make us look for conspiracy. This speaks to Kleiman's point that there is an "eagerness to attribute differences in perception to ill-will".
What to do? Kleiman suggests that he looks for disconfirming evidence, rather than confirming evidence. Silber and Drum both look at antiwar and prowar information sources, and Silber argues persuasively that a responsible person ought to look for and disseminate information on what's going on, rather than evidence that they were right. It's been suggested that scientists should "discard a pet hypothesis every morning before breakfast" to get used to not holding unconfirmed opinions so close to the heart.
So far so good, but I worry about a fragmentation of our news sources making confirmation bias worse. Now that we bloggers have lists of blogs we like and visit frequently, are we in an ever-increasing spiral of confirming our own biases? The filtering function of blogs means that there's an amplification of the tendency to notice only confirming information. I don't intend to point a finger only at blogs. For example, Canada now has the National Post (right wing and more pro-American) allowing the Globe and Mail to potentially be more left wing -- and allowing Canadians to confirm their own biases via their preferred national paper. We have increasing numbers of sites like IndyMedia and Reason and most of us don't visit both. An explosion in news sources may be a good thing overall, but its worthwhile being aware of the dangers too.
Here's an even worse thought, in its way. Taking a public stand is known to increase one's commitment and increase one's desire to remain consistent with that commitment (Cialdini, Influence). Bloggers, anti-war protesters and people who write letters to the editor are all ordinary people taking very public stands. This can be good -- it increases the participation in public discourse. But it can also be bad, making these very people extremely reluctant to change their views. For example, the environmentalist and peace movements both do a great job of getting people active and on the record for supporting the environment and peace. Once people are on the record -- even if it's only a letter to the editor exhorting better recycling in your community, or attending one peace rally -- these people are now less likely to notice information that indicates that a particular invasion might be justified, or that certain kinds of recycling are a waste of resources.
Update: An interesting paper on confirmation bias in anti-biotech sentiment suggests that the structure of the Internet worsens confirmation bias -- people may avoid clicking on links that could disconfirm their position. Too bad the report writer didn't try to disconfirm that hypothesis itself, e.g. through testing.