I forgot to put my iPad on aeroplane mode during a recent flight. The battery did run down considerably during the flight, even though I did not use the plane's Wi-Fi. What's the worst that could have happened? - Anon
Although it's highly likely that a large number of phones are accidentally or intentionally left on in every flight and have been for a decade or so, I've consulted the internet and cellphones can and do interfere with planes.
When a phone is set near a speaker, it creates a "dit-dit-dit" tone that's pretty annoying. You've probably heard this interference yourself but perhaps not for a while. Aeroplane mode turns off the radios on your phone, preventing the issue.
Even modern phones will do this. When reception strength drops, the device will often try a GSM connection to see if they get a stronger signal.