As an Aircraft Engineer, I have seen phone interference on the flight deck. This was several years ago, in the analogue days.
It would manifest as spurious readings and warning flags on the integrated displays. It would only happen with a crap phone in certain locations of the aircraft. Our belief is that whilst "normal" phones and electronic gadgets are sufficiently shielded, meeting the FCC regs, some faulty devices can emit the wrong type of interference.
Incorrect data is the last thing that your pilots need in high stress situations like takeoff and landing, especially if something is not going to plan.
So please, for this and all the other reasons explained earlier in the thread, turn off your gadgets when told to. Its only for a few minutes.