Allow me to shed some light on the subject:
Cellphones operate using a Microwave-band radio signal, mind you of perhaps no more than a watt in intensity during a phone call.
Microwaves of course cause damage to living things, although not as rapidly as ionizing radiations like those of nuclear origins. Those damages usually result in either thermal-like effects such as radiation burns, or molecular damage resulting from radiation interacting with matter.
So while a casual user will never realistically expect to see a significant difference in a measurable timeframe, it is still a potentially damaging radiation in measurable levels. People who recieve high doses of this radiation through chronic long term cell phone use will indeed experience an elevated risk of health problems as a result of the radiation recieved.
But considering that modern phones have such a low power output because of the dramatic improvement in transmitter and reciever technology in the past decade, the amount of radiation damage done by the average cellphone would be most likely less than the damage done by natual radiation sources such as Radon gas and Carbon/Iodine isotopes found in all organic materials.
So yes. Sound the alarm put on the tinfoil suit these phones emit dangerous radiation. But no, the amount of radiation they produce is tiny compared to how much you get from other sources such as microwave ovens, medical radiation, and natural processes.
As far as predicting earthquakes go, I could see it done the same way I calculate how much strain a piece of metal will take before it snaps. But for that to happen a few assumptions must be made: That the material is uniform in composition and strength, that the applied load is known, and that the temperature and pressure at time of failure are predictable.
The problem is this: That kind of model only works when you can safely make those assumptions.
The earth's composition is not uniform, it varies a great deal even among different sections of the same piece of rock. It would take a phenomenal amount of measurements to even approximate that level of variation, well beyond practical budgets and labor pools.
We can only ever guess at how much strain a given piece of rock is holding. In metals, you can measure how deformed a piece of material is to determine how much strain is on it before it breaks. But because rocks are non-uniform, this approach cannot be used because the rocks will not deform in the same way every time.
And of course, we can't control the weather or how many other forces are being applied to the fault in question.
So although it is theoretically possible to make a good guess, the amount of measurements and computing power required to accurately predict such a thing is beyond what is available.
These scientists should countersue using a similar arguement to prove their innocence, and claim damages money (to be used improving the science of course).