Ben Goldacre and others carried out a very interesting study: they analyzed the top 10 UK newspapers for a week for their health reporting, and categorized the quality of the support for health claims. It's not encouraging.
Here's what we found: 111 health claims were made in UK newspapers over one week. The vast majority of these claims were only supported by evidence categorised as "insufficient" (62% under the WCRF system). After that, 10% were "possible", 12% were "probable", and in only 15% was the evidence "convincing". Fewer low quality claims ("insufficient" or "possible") were made in broadsheet newspapers, but there wasn't much in it.
I do have one criticism, though. The paper is in a journal called Public Understanding of Science. It isn't open access, though, so apparently the Public is not allowed to read about the Public Understanding of Science unless they cough up $25 per article. They can read about "science" for cheap in their local tabloid, though. Isn't this part of the problem, too? Let's also put part of the blame on a science publishing industry that puts up barriers to reading the real stuff.