What are a couple of advantages of having a liquid cooling system over an air cool system,

To be more to the point, there are more advantages to having an air cooled engine, less moving pats, such as fans and water pumps, less weight in the engine construction no hoses, radiators that can fail and damage the engine, air cooled engines are light smaller in construction, the heater systems are just as good or better then water cooled engines, with that said, air cooled automotive engine are not best suited for large capacity engines as the cooling efficiency is not as good as water / coolant but is perfectly suited for small capacity engines, just as a note, large radial aero engines are well suited to air cooling as the atmosphere they operate in is much colder and the slipstream of the props remove vast amounts of heat, this is just not possible in larger automotive engines, i hope this helps.