The raw water pump pulls seawater in to cool the engine and the exhaust. When it fails, the engine overheats and the exhaust hose can overheat and burn through. When it leaks, salt water sprays over the front of the engine and corrodes everything below it. Either way, a surveyor wants to see it dry and pushing a good stream out of the exhaust.
How a surveyor checks it
Before starting the engine, look at the pump. Good Old Boat's key sign: most raw water pumps have a small weep hole on the body, and water dripping from it means an internal seal has failed. Look for rust and salt crystals on the pump, the engine bearer and the drip tray below. In the author's case, a slow drip had left rust under the pump.
With the engine running, look over the side at the exhaust. Good Old Boat advises doing it routinely: water should come out with the exhaust in a steady pulse. A weak or intermittent flow means the impeller is worn, the strainer is blocked, or the seacock isn't fully open.
Then the records. An impeller with no record of being changed is due, and a spare should be aboard.
What decides the grade
Flow. No cooling water, or an engine running hot, is an A: the engine shouldn't run until it's fixed. A steady drip from the weep hole is a B, because a leak past the water seal will eventually find the oil seal and the bearings. An impeller with no service record is a C.