You should only have to apply it to the CPU. Thermal paste is used to fill the microscopic gaps between two surfaces of metal. Unless either surface has a gouge in it, or is uneven, you should only use a very, very thin layer of grease. If either surface DOES have a gouge bigger than a hair's width or is uneven, it's probably defective anyway and should be replaced.
Using too much will eventually bake off all the grease and the 'cake' that's left will become a heat insulator instead of a conductor.
Using too much will eventually bake off all the grease and the 'cake' that's left will become a heat insulator instead of a conductor.
