Boiler failure - just as a water heater can fail, the boiler can also develop leaks. The good news is that since the water is enclosed in the system and is typically not replenished on a regular basis, there is not a significant build-up of calcium in the tank as there is in your hot water tank which continually brings calcium into the water heater. That calcium settles in the bottom of a water heater and causes hot spots and eventual failure of the water tank - not so with the heating system's tank. Leaks in the system - normally obvious in the form of wet floors or carpets underneath the baseboard units. Air trapped in the system - causes a gurgling sound in the system when the circulator is pumping water.
Overpressure valve blows off - caused by the air being removed from the expansion tank.
The leak must be repaired and the system drained until the air is replaced in the expansion tank . Dust in the radiator units - the radiator units are typically made up of copper tubes with fine sheet metal fins attached. These fins get clogged and need to be cleaned with a vacuum cleaner. One of the major shortfalls of a baseboard heating system is that there is no way to install central air conditioning systems, air filtering system or whole house humidifiers. The upside is that they are quiet, and clean since they don't blow air all over the house.