The most famous indicator of a waning radiator is overheating or even unusually high engine temperatures. This can originate from incorrect coolant levels in the radiator. Coolants are avenues of escape of the heat generated by the engine. The radiator makes sure that the coolant doesn't get too hot once it goes back to the engine. It's always good to have a full coolant reservoir, especially on dry and hot seasons. Similarly, any contaminants that can get caught within the lines and the coils in the radiator could contaminate the coolant and hinder its job of alleviating the heat from the engine.
As the car gets older, the radiator and its parts can get worn out. Leaking is one of the earliest signs of this. Any leak coming from the radiator is bad news. You can detect this by a distinct sweet smell or green liquid directly below the engine where the radiator is located. If this happens, there might be holes in the radiator or the hoses. This can also happen if some freak accident happened to puncture your radiators. Either way, worn out parts must be replaced immediately.
The radiator might be one single block of an engine component but a lot of internal parts work together to make sure that it does the job of cooling the engine. Since it is exposed to high amounts of stress, a bunch of defects can affect the radiator. This can result to more problems for the vehicle. For one, if the thermostat of the radiator fails, the radiator won't be able to properly regulate the temperature of the vehicle. Another example is a broken and loose cap. Aside from not letting any debris get inside the radiator, the cap also regulates the pressure inside once it gets pretty hot. The seal at the underside of the cap is made of rubber, which easily gives up under stressful conditions. The presence of rust and corrosion is not a good sign, especially for the radiator. It can eat up through the metal and mess up with the water and coolant flow.