Mobile phones DO cause interference with systems. I know this from experience.
1. When I was doing my private license, I had my phone in my bag in the back of the plane and on the day of my first solo I was nervous and forgot to turn it off. On finals I got interference in my headset when my phone started ringing.
2. About a week ago I was making my landing PA from the aisle seat on the A319 when the cabin address system started buzzing. It turned out that the guy in 21D was trying to make a phone call.
If phones can interfere with the simple electronic circuits in address systems and headsets they are almost certainly causing unknown havoc with the incredibly complex electronics in the average Boeing/Airbus.