Look for crash scrapes on the mirrors, indicators, bar ends, lever ends, exhaust, seat unit and the bottom of the forks (bodywork damage is usually obvious).
If it has been down the road it’s not the end of the world, if it has been properly repaired. Fork, swingarm and frame alignment all need checking. It’s best done on a jig, but running a plank down both sides of the rear tyre and seeing how it aligns with the front gives a fair idea.
Wheels that aren’t parallel could just be uneven chain adjustment - check. Pump the forks down and up with the front brake on and watch for twisting.
Be suspicious if the bike has been ‘warmed up’ before you arrive. It may hide starting problems and giveaway noises.
Ask the seller to start the bike for you. If he doesn't know how, it’s not his bike, is it?
Let the engine tick over and listen for knocking low down in the engine. It could be a big end or main bearing about to let loose. RIP engine.
Up higher, listen for loud, fast tapping indicating worn tappets, incorrect valve adjustment or even a worn-out camshaft. Replacing cams and tappets is expensive, lack of adjustment shows a careless owner.
Blip the throttle a little. Black smoke with a smell of oil could mean piston rings or valve guides are shot. Leaking oil, especially from the cylinder head, is never good.
Pump the forks up and down with the front brake on. Oil left on the stanchions mean the fork seals have gone and suspension damping will be dangerously poor. Replacement seals are cheap; labour isn’t. And rust or stone pits mean seals won’t last five minutes. You’ll need a front end rebuild.
If the front end is really springy, the damping oil may have gone entirely.
Do the same with the rear end, looking at the shock(s) this time.
Ensure the handlebars move right and left smoothly with no noises, otherwise the bearings are shot. During the suspension check, there should be no movement fore or aft at the headstock.
Roll the bike forwards with the front brake on. Do the same with the rear. Are the discs warped? If the brakes work OK, check the pad thickness and look for scoring on the discs.
Lean across the seat and check the chain. There should be about 30 mm of slack. Roll the bike around, checking for any tight spots. Check the sprocket’s teeth. If they’re pointed, it needs replacing.
Are they a pair? Minimum tread depth is 1 mm but you should replace at anything less than 3 mm. Check both tyres for perishing, cracks, splits or nails.
Accelerate, brake front, brake back. Does it run straight? Are the brakes strong? Any strange noises? Stop it then start it again. All good? Start haggling.