I had been under the assumption that the real reason why the FCC doesn't allow cellphone usage on commercial flights is because the phones have the potential to screw up ground towers since the phones are rapidly hopping between towers while in flight, not because the cell phones had any real impact on flight control systems.
An article in the March 2006 issue of IEEE Spectrum strongly argues that cell phones and other personal electronic devices do indeed interfere with aircraft control systems such as those that rely on GPS. The researchers argue that if FAA restrictions against cell phone usage in flight are rescinded, that in all likelihood there will be an accident caused by interference with cockpit navigation systems. The authors state:
Our data and the NASA studies suggest to us that there is a clear and present danger: cellphones can render GPS instrument useless for landings.
They also argue that their data supports the contention that cell phone usage has already caused aircraft accidents.
The researchers also discovered that despite current rules, cell phone usage aboard commercial aircraft is widespread, even during critical takeoff and landing phases of flight.