Can it breathe?
Make sure vent hoses aren't crimped. Underway, try lifting the engine hatch. It should lift easily. If there's suction, it means the engine is starving for air.
Check that the engine's numbers match those on the contract. Look for engraved plates riveted to the block. You may need degreaser to read them.
Turn the steering wheel from lock to lock. More than seven turns may mean a leak or low fluid. Look under the boat -- rudders should fully turn to their stops.
Check to see if the hydraulic steering pump is the right size. Get the pump's model number from its engraved plate and compare it to the manufacturer's literature.
Throw the levers on every seacock. Do plumbing, stringers, or anything else block them from opening or closing?
All raw-water intakes need to have two hose clamps on each end.
Strain is good
Raw-water intakes, especially for engine cooling, should have South Bay external hull strainers or basket-type strainers inside the boat. Baskets are better as they can be cleaned from onboard. Ones with a clear bowl show what's going on inside.
Secure yourself in the engine room and have a helper throttle hard in reverse, then in forward, one engine at a time. Watch the motor mounts for deflection -- anything more than ¼" is a problem.
Look to see if the threaded studs of each motor mount are centered. If not, something's out of line.
Run the engine at full throttle underway to be sure it turns up -- gets within the manufacturer's maximum rpm range (get this online or from brochures). Under- or over-revving could mean the wrong prop was installed, which can lead to excessive engine wear.
Exhaust risers should be at a height above the waterline per the engine manufacturer's specs to prevent back flooding. They should be connected to the transom by a flexible coupling to keep from vibrating loose. The entire exhaust run, which is filled with water and therefore heavy, should be robustly secured and supported.
The prop shaft's flange and the one from the transmission must meet evenly with no gaps and no offset. Use a feeler gauge to check.
On inboards, measure the distance from the hull to the tip of the prop. This should be at least 15 percent of the prop's diameter -- more is better. Any less and there's a chance of "hammering," an annoying harsh vibration felt while underway.
A good tip
Rotate an inboard's prop to make sure that each tip is the same distance from the hull. Rest a block of wood on the hull and to the side of the prop and measure from tips to block. Any unevenness in either test means an unbalanced prop.
Inspect the type/size/quantity of fixed fire extinguishers. Compare against the Coast Guard's regulations for your boat type at: uscgboating.org/safety/fedreqs/equipment.htm.
Verify the operation of the automatic fire suppression system. 1) Start the engines and look for a green indicator at the helm. 2) Disconnect the plug from the fire suppression system cylinder. 3) Verify that the red light comes on, the alarm sounds, and the engine stops.