Running a damaged propeller can cause bigger problems. A propeller may only appear lightly damaged but could still be out of balance. When your propeller is even slightly out of balance, it will prematuraly wear out propeller shaft seals, bearings and the propeller shaft itself.
Running a damaged skeg will affect your boat's steering and overall control. Your skeg also protects your propeller.
A damaged cavitation plate will allow the propeller to suck air from the surface of the water when the boat is on plane. This will cause cavitation, the propeller will slip, and the boat will lose performance.