(Repeating something I posted in Jan04)
The CAA published two papers on the subject:
Interference Levels In Aircraft at Radio Frequencies used by Portable Telephones
looks at the electric field strength in various parts of aircraft caused by a mobile phone in other parts. The highest field strength observed was about 4.5 V/m in the flight deck when a 2W 900 MHz phone was used in the forward cabin of a 737. This would exceed the limits in the certification standard of equipment before 1989, but not more recent equipment. Avionics bay fields reached about 1 V/m.
Effects of Interference from Cellular Telephones on Aircraft Avionic Equipment
reports on experiments in which a number of pieces of avionics certified to the older standards were subjected to field strengths of 30 and 50 V/m, equivalent to putting a mobile phone about a foot from the equipment. Unsurprisingly, they found the equipment misbehaved from time to time.
I have to say that this doesn't strike me as a significant body of evidence indicating a problem, but nor is it an all-clear for mobile phones.