Shy Torque has it right. The issue of using any emissive device on a flying machine is one of EMI, electromagnetic interference. We flight and ground test all equipment on the aircraft to see what is affected, and we either shield, placard or restrict the offending devices.
Because we haven't tested at all, some chance of improper operation of ship's equipment is possible when the cell phone (or computer, PDA, calculator, etc.) is used. The worst offenders are the emitters by design - radios and cell phones - so these are prohibited throughout the flight. Other electronic devices send out weaker signals, and so are allowed during cruise, but not when on approach or departure (where a wiggly ILS needle could get serious).
In reality, the chances are small, and the threat is tiny, but since we pay tickets to be passengers, not lab rats for the guy next to us, public safety makes it easier to ban the devices than to qualify the aircraft with all manner of posible toys.
When we test for EMI, lots of funny stories are generated. the HF radio is especially a problem due to its high emissive power and the wide frequency range. Many wires and lines on the aircraft become antennas, and if the wire length matches the wave length of the emmitter, funny things can happen. I had the gear drop on one aircraft each time I talked on the HF, and on another, the nav displays began flipping seriously. To prevent or cure EMI, we overbraid the harnesses and run that braiding to aircraft ground to shield the wiring. In severe cases, we use special band pass filters in the wire to block offending frequencies (filter pins).
Note that your computer emits, and the steel plates that mount on the holes in the case should be fitted to prevent stray signals from interfering with TV and radio reception (again a remote possibility.)