Yeah, the MythBusters pretty much demonstrated that radio signals from mobile phones
can influence navigational equipment… particularly the tracking of
VOR stations and/or
ILS signals. Their experiment showed a
CDI swinging pretty wildly when the radio signals were turned on and off, I believe to the point of going back to its default position when no VOR signal is being tracked. Somehow, I think having the ILS start going wonky when you are coming in on an autopilot landing can be problematic, especially if the pilot is not prepared to take manual control immediately.
These experiments were done in a Faraday cage to exclude all external radio signals, and all the avionics wiring was completely unshielded. I do not remember how they produced the VOR signal inside the Faraday cage, but it worked somehow. They were not able to replicate the results in an actual aircraft, which has shielded avionics (and had to remain on the ground due to FAA regulations).
So, it is generally regarded that using a mobile phone while in flight won’t cause too much trouble, but the FAA seems to want to play it safe anyway. Probably a good idea as there actually may have been an aircraft crash where a cellphone signal played a role:
Crossair Flight 498: Alternative Theory.
Of course, the ban on cellphones is in flux right now, and changes may be on the horizon:
Mobile Phones on Aircraft.