A few years ago, a group of engineers from the IEEE flew a portable spectrum analyzer that monitored RF emissions on 37 commercial flights (with FAA permission and the assistance of 3 airlines). They found that between one and four mobile phone call were made per flight and that at least one passenger forget to turn of his or her mobile per flight. Furthermore, they found emissions in the GPS frequencies from PEDs onboard. Their conclusion was that in normal use cases, PEDs will not interfere with aircraft hardware but under worst case situations, a PED can interfere with a aircraft instrumentation. One of the issues pointed is that the FAA and FCC do not co-ordinate their rules. Phones that operate according to FCC limits can produce spurious transmissions in frequencies that encroach on the safety margins of flight equipment. If the US government really wants to allow expanded PED usage, the FCC should introduce into its rules limits for PEDs in aviation equipment frequencies.
Read the article for yourself:
"Unsafe at any airspeed?"
IEEE Spectrum, March 2006
There are few updated articles:
"Electronic Devices, Airplanes and Interference: Significant Danger or Not?", IEEE Blog post, 18 Jan 2011
"Do Mobile Electronics Really Interfere With Flight? They Could" IEEE Blog post, 3 Feb 2011
We know that PEDs can interfere with aircraft electronics. NASA maintains a
database of voluntarily submitted incidents that did not result in a crash. There is a report (ACN 475267) of a Toshiba laptop being used by a person sitting in a certain row (the online report censors the row number) produced RF emissions that caused the VOR needle to spin. The flight attendant had the passenger shut the computer down and the VOR began to operate correctly. The pilot asked the passenger to power it back on and this time the VOR needle indicated a 40º deviation from correct heading. When the passenger shut it back down, the VOR indicated the correct heading and they continued the flight without the computer turned on.
I am not aware of any accidents being caused by a PED so far (but that doesn't mean one hasn't happened).
One thing I haven't seen in this discussion so far (although the discussion is about PEDs in general) is the effects on the cellular system of mobile phone use in air it is my understanding that a large number of people using mobiles while in flight will wreck havoc on the cellular system. The current system is designed for people using phones in cars with highway speeds. An airplane travels much faster and the call will transfer from tower to tower rapidly and a large volume of these rapid transfers could take down the cellular system. This is why picocells are needed to use mobiles on commercial aircraft (but I don't have a cite for this).