Can passengers use headphones during takeoff and landing?
Jan Hudec was right.

Passengers are not to wear headphones during critical phases of the flight (understand : takeoff, landing, taxi, emergencies), because this could prevent them to hear announcements or directions made by the crew in case of emergency, and because headset cables could create an obstruction in case of an evacuation.

Also, this would prevent them from listening to the safety briefing.

This safety rule is enforced, as far as I know, by several European airlines.