There have been numerous threads on this topic, so I apologise for boring some of you who may have read this before!
My guess is that if there are more than (say) 20 pax on board there's a better than evens chance that at least one phone is active throughout the flight (whether by accident or design). More than 100 pax and it's practically a certainty. Since we do not observe any serious problems that have arisen as a result, this would indicate that such problems are very rare, if not impossible.
Airlines (now that they can make additional revenue from it) are offering the ability to use your mobile in flight. This is done by siting a 'pico-cell' on board, allowing the phones to operate at their lowest power setting. Someday this pico-cell will fail, at which point all the active phones will automatically boost their signal to the max in a futile attempt to contact the nearest base station 10 kms below them. This will be an excellent test of the aircraft's susceptibility to EM interference. My guess is that nothing will happen (see above) - what's your guess (and would you want to be on board when this 'experiment' takes place)?