i dont think there is anything wrong with the unit. dirty coils dont cause a unit to continue run. the unit is controled by your thermostat. The stat has a temperature sensor in it monitoring the air temp. in the surrounding area
for example: if your stat is in direct sun light or the area it is in tends to be warmer it might think the room is 80 degrees even though its only 70 degrees. The problum is in the stat. look into that first. although clean your equipment is good and should be done every year. filter, coils cleaning, ect. hope this poinst you in the right direction