Garage
Check the action of the garage door and look for dents in the tracks or cracks in the door.
Make sure tool storage and hanging rakes and shovels don't create a falling or tripping hazard.

Kitchen
Test the drainage of the sink and look for signs of leaks on the faucet.
Look at all the cabinet doors and drawers to make sure they open and close properly. Check for loose hinges or sticking drawer slides.
Turn on the disposer and listen for signs of obstructions or problems with the motor.
Try all the stove burners to be sure they turn on quickly and properly, without sparking or bursts of flame. Make sure gas stoves give off an even blue flame.
Check the oven door gasket for signs of wear and tear.
Turn on a gas broiler to make sure it lights properly.
Make sure the gas shutoff valve is working. It should be able to turn until its completely perpendicular to the pipe.
Open the dishwasher and spin and lift the washer arm by hand to make sure it isn't stuck. Check that nothing has dislodged the drain hose; it should arc up to prevent backwash from the drain into the dishwasher.
Look for signs of leaking under and around the dishwasher.
Make sure water filters have been changed recently.

Download a printable version of the entire Yearly Inspection Checklist here.

See some of the crazy things house inspectors find in Home Inspection Nightmares.
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