Apart from actual leaks from the radiator caused by internal rusting creating pin hole leaks and leaks caused by poor seals where the valves are connected to the radiator , the only other faults that affect radiators are :-
1) If the radiator is cold along at the top , then air has dissipated from the water in the system and accumulated in the top portion of the radiator and the radiators need bleeding to release this air and the central heating system needs re-pressurising. The central heating is most efficient when the pump is pumping around non-compressible hot water, when air separates from the water in the system due to heating the water, the water is non-compressible but the air can be compressed by the pump, this situation makes the pump very inefficient and the heating system becomes virtually useless.
Radiators should be bled as and when required and the system re-pressurised to compensate for the volume of air released by this process.
2) If the top of the radiator is hot and the bottom part of the radiator is cold, then the system is full of gunge and the radiator cannot function correctly. The central heating system will need to be power flushed to remove the grunge and silt clogging the system as the pump will not be able to efficiently pump the hot water around the radiator network, this is a job best left to specialists.