buying a used outboard
Yep, compression and gear lube are the most important. I'm about the last guy you want to deal with when selling your used outboard, but here's my .02.
Tell the buyer to leave the engine cold (assuming you can run it, if not, skip most of this) and be sure it has good fuel. Show up and have him start it for you (on a flush attachment or in the water), this will show how hard it is to start etc..
Once it warms up, listen for anything obvious - odd noises, excessive stalling when warm or excessive vibration etc. Smoking is OK - means nothing w/ 2-strokes. Be sure it's pumping a good stream of water. Shift it a few times in and out of forward and then in and out of reverse, it's quite loud doing this out of the water, but shouldn't excessively grind for periods of time. When the engine is in neutral, the prop probably should not excessively spin, slowly is OK, but if it appears to be in gear and is in neutral, make note when checking gear lube; this can mean nothing or that something is binding up in there. If the engine cannot be run, the prop should spin freely in neutral.
Best thing to do is take it out for a beat run on the water, at wide open throttle for 20 minutes or so. When bargain shopping, that's not usually possible, so just bring the RPM's up a bit and be sure all seems in order.
Check the compression with a warm engine if possible. If it is not possible to start it, pull the plugs out and jump the starter solenoid. Depending on the engine, 110 at the lowest cylinder is a good engine w/ no more than 10 psi difference in clyinders. 100 is OK and 90 is fine for some OMC's. 15 psi difference is OK, if the cylinders are all spread out, if all are 115 and one's 100, I'd think twice about it. Sometimes a decarb treatment can make quite a difference though in compression - walked on two OMC 150's (dirt cheap) last spring, due to bad compression, and my friend picked them up to find after decarb - compression got even and went up 20 psi!
Look at the plugs; make sure there are no obvious signs of water in the cylinders. This is hard to spot for sure, but it happens.
Drain some gear lube out; It should be clearish, not milky, rusty, or black, but tinted as it looks new, and should not have any metal chips or water or excessive black dust etc.. Some metal hairs on the drain plug are normal, but if there is a massive clump of them there and they are present all over the lube, it probably got run dry.
Take a look for excessive corrosion. On merc's, be sure the lower engine mounts are holding up. The upper bolts on old OMC's can go. Take a look around the powerhead for snapped off bolts, especially on the head. Just be sure everything looks in place, no coat hanger on the throttle linkage etc..
If you took a hard enough look, you surely found something wrong. Bring it up when you discus price. Good luck,