There are quite a few things that can go wrong with rads in your house and not all of them will be pleasant but you have to get dirty to fix stuff yourselves otherwise get a plumber in a get it fixed properly. With all things a proper diagnosis is often the quickest route to fixing a problem. Radiators in the main are made up of pressed steel and can also be tubular steel like column rads. Water runs through the main waterways of a radiator and the main issue is to do with leaks but there are more described below.
Leaking rads are caused either on installation or when they are old and corrosion has caused the steel to puncture or split. If you are experiencing leaks on newly installed rads then I would be worried as there is not enough PTFE on the valves or you have a defective radiator. All radiators are quality tested and this has become an exact science today as the amount of leakers on installation is extremely rare and almost non-existent. Rads that leak after a period of time are unfortunately down to corrosion and this can happen in a very short period. It is always important to fully protect the system with an Inhibitor like Adey MC1 Protector.
Radiators that are not getting hot can be down to a number of problems and the first thing to do is check the pipes are hot going into the rad. If this is the case then something is stopping the hot water entering. This could be the thermostatic valve or standard valve and may just need a knock or turning up and down to stimulate the valve. Air also stops water entering into to a rad so try venting through the air vent. Sludge and debris can also build up in a rad to give an impression of cold spots and will generally sit in the middle of the rad and the water will flow around it.
Noisy rads can be caused by air and also velocity of water in the system and a remedy is too vent the radiator and make sure that you have the plastic clips located on the brackets that stop movement. If these are missing then you can use tape or something similar.