In the does-it-or-doesn't-it department, the World Health Organisation reports on whether mobile phone use is carcinogenic (cancer-causing) (discussed here and here, among many other places). The WHO says they can't prove, but cannot rule out, a carcinogenic risk from heavy phone usage. Many or most studies have not found a significant link--that is, that callers have a rate of brain cancer that is surprisingly higher ('statistically significantly' higher) than would be expected by chance alone, but some studies have found enough evidence that there may be some connection.
The problem is that any such risk is very small so that large samples are needed to find significant effects, if indeed such criterion--unusualness--is the right one for evaluating this kind of thing. If you need a huge sample to demonstrate an effect, you immediately run into several major issues. First, what you want are large numbers of subjects who are identical except in their phone usage. But of course no two people are identical, and they vary in many ways.
Second, subjects need to remember their usage over many years, so that their exposure can be quantified--because there is surely going to be a dose-response pattern (how much exposure, not just yes/no). But who can remember in sufficient detail or with enough reliability? There are likely to be age and even sex-specific effects, so that acquiring enough similar individuals to allow the investigator to categorize as necessary is a challenge. And subjects would have to reliably report which ear they used to listen with and so on.
Third, phones themselves as well as usage patterns have changed. And fourth, different populations (countries, etc., from which samples are drawn) will have their own variation in these same variables.
Cancer is a largely genetic disease at the cellular level. Mutations activating or modifying the wrong genes, in the wrong combination, can transform a cell that then is the progenitor of a clone of descendant cells that comprise the cancer. So evaluating cancer risk presents the same kinds of problems that any gene-function (or gene-evolution) connection presents. In reconstructing evolution, such as the genetic basis of human smiles, sweat, sex in flies, or the way that bats evolved echolocation, nobody cares if you guess wrong. But when it comes to cancer, we care very much!
But it is not just us who care. Cell phone companies care, and not necessarily for salubrious reasons. Science journalists and scientists care because there's business to be made in getting large research grants, and writing dramatic news stories. For example, is it right or is it exploitation for CNN to post model-specific energy emissions? It's certainly a form of sensationalism, especially since the differences may or may not be correlated with risk in ways related to the current WHO report, and because who of us knows what to make of our phone's radiation number? Or is it a public service: if your Droid or Blackberry is a high emitter, you could junk it for a Nokia or deprive your kids of smart phones, and that may smart.
And of course this kind of story is great for grant agency administrators who want the research portfolios to manage, and so on. So we quickly find ourselves out of 'clean' epistemological territory with such an issue as this.
Weak causation is very difficult to determine generally, as we state many times in MT. And of course there is the question whether a small risk would deter you from using your mobile. The risk of dying in a car accident is probably far greater, but we don't seem to be ready to turn in our keys....