The most common faults are

Power cable break. Because of the way it swivels, the joint wears and you get intermittent or complete no-power.

Thermal Fuse. Often the plug fuse (UK) will blow also. The symptoms are the unit not powering on at all. Quite often a faulty thermistor will cause the thermal fuse to blow. So if you only change the thermal fuse, it could blow again. To be safe, change the thermistor at the same time as the thermal fuse

Thermistor. Usually the unit powers on and beeps, but no heat in the plates, unless it has also caused the thermal fuse to fail, in which case see bullet point above

R8/R11 Resistor failure on mk4 and mk5 is VERY common. Easy to fix but can also cause heater element to fail as well. See this link for more details

Other common faults can be found at this link.