I thought it was interesting that they pulled out the old physicist trope, "X-rays generate radiation that causes cancer. Cell phones don't generate that kind of radiation. So it's unlikely they cause cancer" (paraphrase of a quote from the article). That's wholly unconvincing. It's assuming there's only one mechanism leading to cancer: high frequency radiation. We actually don't know much about the relationship of low-frequency, low-power radiation and cancer. More importantly, there could be a mechanism that is unknown to physics and biology which could make cell phones cause cancer. For example, we do know, for a fact, that using a cell phone heats the tissue surrounding your ear, and that the body has known heat-damage-response pathways that when activated, lead to tumors. So that alone is a plausible mechanism that should be studied further, presuming the epidemiological studies show there is some correlation between using a cell phone and having cancer, that can't be more easily explained by other factors, such as lifestyle or other forms of exposure.
That said, the followup point about epidemiological studies is also pretty suspect. The phone technology has changed dramatically over the years, and much of the studies are based on self-reporting. No carefully controlled clinical trial has been carried out. However, the studies that have been carried out do suggest, if not prove, that the increased incidence of cancer, if it exists at all, is a very small effect, barely statistically significant even in a well-controlled, high-population study.
Making policy like Berkeley is doing just isn't supported by the science- there are far more risky things in Berkeley, like inhaling secondhand smoke on Telegraph or driving on Ashby.