I don't know if it's still an issue, but at one time the cell phone providers didn't want people using their phones on aircraft because at cruise speeds the phones switched between towers too frequently to be reliably tracked (and of course billed, which was the real concern).
Modern aircraft are rather well shielded for Electro Magnetic Interference (EMI) - initially it was done by FAA "Special Conditions" (and the JAA equivalent) - now days it's been incorporated into the FAA FARs and EASA CSs. Since I worried about engines and FADEC (which are outside the pressure vessel) we had to meet higher levels than stuff inside the fuselage (which helps shield external sources) but the EMI limits are still high enough for flight critical systems that a 1 or 2 watt cell phone transmission inside the fuselage is still insignificant (unless the shielding hasn't been properly maintained, which is a concern and not just for cell phones).
Years ago, Boeing received many reports of 'unusual' flight deck effects or displays that went away when the cabin crew told some passenger to turn off their electronic device (often reported to be video games). Thing is, the Boeing EMI group worked with various operators, and would have the airline buy the (apparently) offending device from the passenger and return it to Boeing. According to my friends in the EMI group, they never were able duplicate the problem or even find unusual emissions from the returned devices.