There are actually some studies conducted. Note that these are _suspected_ interference from personal electronic devices and also incidents with passengers unwilling to turn them off: http://asrs.arc.nasa.gov/docs/rpsts/ped.pdf

Of course, all of this is anecdotal so it won't fly here on HN. :)

The real difficulty is that when an instrument malfunctions, that can be for any number of reasons. It's not unusual for malfunctions to occur, which is why airplanes have redundant avionics. However, there seems to be a few instances where the interference stopped after a passenger turned off their devices.

Well in my experience, small incidents are quite common, maybe a pilot can experience 4 to 6 a month. The hard ones are quite rare (thankfully) something like 1 every 2 or 3 years, maybe less(for a pilot flying 900 hours/year). But this is far from hard data, more like pilot and engineering informal chat. There is maybe more than the cell phone factor here, other problems involved that are hard to detect like a sensor with a corrupted signal, a bad cable (some miles of them at a plane), a software bug. I don´t think there is an easy solution. Thankfully it is very rare that this happens in a delicate situation (like a cat III landing with 0 visibility), and even then you can go around and call the passengers to disconnect their cellphones. It is not like a terrorist can come with a super evil cell phone and kill everyone that easily. But is a safety concern none the less. I wouldn´t recommend that politicians legislate about this randomly.