When it comes to weird results in human epidemiology and public health, my bet is always on hidden/unknown 3rd factors. You're right that the signal might be real, but it might have nothing at all to do with cell phones. Rather, cell phones might be independently correlated with whatever the real causes of the sperm problems are.
Put in plain English: a group of men with similar cell phone habits probably have many other things in common.
yes, I think it's always key to look at epi studies like this and make absolutely sure everybody agrees the protocol is designed to address bias. I'd say only about 10% of the studies I read do this adequately (it's one of the things that helped convince me Ionnides is right that nearly all studies are Just Wrong).
It is impossible for an epidemiology study to elimate hidden factors, no matter how many statistical tests they run. Hidden factors are hidden, which means the statistics can't tell you about them. Information not available to the researchers cannot be evaluated by the researchers.
This is why the concept of a mechanism is important in science--it provides a framework for simplified experiments that exclude hidden factors by their design. For example if the hypothesis is that cell phone radiation causes sperm problems by damaging human cells, then human cells can be directly exposed to that type of radiation to see what happens.
Like I said, a carefully designed study can eliminate many biases. I didn't claim it could eliminate hidden factors.
Anyway the problem with finding something in an epi study then trying to reproduce it in a minimal environment (isolated cells exposed directly to radiation) is unlikely to uncover any complex mechanism. Cells on their own don't behave like tissue, and tissue on its own doesn't behave like an organism.
Even doing radiation tests on rats in a lab is going to have fewer confounding factors than 100 infertile human guys filling out a questionnaire.
I'm not aware of any lab rat studies that found harm from cell phone radiation. And of course the basic mechanism by which radiation affects materials is pretty well understood.
All this is to say: I think yummfajitas had it right. Fajitas are delicious.
There are a number of experiments where researchers have reported visible changes to sperm morphology. Here are the ones I found without looking to hard (only extracted abstract; did not read full paper from the perspective of a grad student preparing for journal club)
http://large.stanford.edu/courses/2012/ph250/ferguson2/ "An experiment by Yan et al. in 2007 was conducted to see how cell phone radiation affected sperm quality. [10] The rats were placed in a PVC holding tube and exposed to a total of 6 hours of cell phone radiation per day for 18 weeks. After the 18 weeks were over, the rats were euthanized for tissue testing. They found that sperm motility was significantly different between the control and experimental group. [10]"
That ref is http://www.ncbi.nlm.nih.gov/pubmed/17628553, "Rats exposed to 6 hours of daily cellular phone emissions for 18 weeks exhibited a significantly higher incidence of sperm cell death than control group rats through chi-squared analysis."
Put in plain English: a group of men with similar cell phone habits probably have many other things in common.