Heat in rear but not in front in 2002 Ford Explorer

I'm suspicious of it being the front blend door actuator, stripped plastic gears and such often click when they're worn but there is always the possibility that the blend door itself (looks like a flap) is stuck causing the actuator to skip.

Your vehicle has two heater cores, obviously your rear one is working fine, the front one has a problem with either the blend door actuator or the blend door itself, as poster above states.