Although there is no way to test-run a junkyard engine–before or after you buy it–short of installing it in your car, there are some common-sense checks you can make to avoid buying/using a bad one. You can easily remove the valve cover and oil pan to check for sludge buildup, metal shavings, and grossly worn bearings. At a “you pull it” yard, you can remove the cylinder head to check for cylinder bore wear, nicked or damaged pistons, etc.
Of course, you will want to have the head(s) reconditioned by a professional machine shop, replace all seals and gaskets, replace the timing belt/chain and associated hardware, etc. Some people would say that when installing a used engine, you should also replace all of the core plugs, even if
they don’t appear to be leaking.
As another poster already alluded to, it is very difficult to install a different type of engine into a modern car. There are some people who claim that you can put any engine into any car, but this is easier said than done. I can remember when the Chrysler 2.7L engine was out, there was a lot of interest in putting a different (cheaper, more reliable) engine into these cars. Some people talked about putting the non-interference 3.5L from 1993-97 or the 3.0L V-6 into these cars, but that ended up being much harder than it sounds. Most of these 2.7L-equipped cars went to the junkyard with the body in excellent condition, whereas the 4-cylinder versions of those cars are still driving around.
If it is only one tooth off, I’d be inclined to think that the valves have not hit anything. If it is one tooth off (or more), I’d want to know why. Is it because the mechanic did not get it properly aligned when re-assembling or because it skipped a tooth while running.
If the engine has a marker on the harmonic balance to indicate when it is top dead center, then you can just pull the valve covers to see if the valve timing is correct by check the markers on the cams. Many newer engines no longer have a way of indicating TDC by the harmonic balancer so you either have to find it by removing the front cover or using one of the methods through the #1 spark plug hole. Removing the front cover is more reliable.
Update: I tried turning the crank by hand this evening. It was able to turn a full 360 degrees. In fact I tried turning a full revolution 3 times just to be sure. It’s definitely not locked up because it turned fully and had resistance when turning. My question is: is this enough of a test to verify the motors still good? If so I’ll probably fix the timing to get it running and then sell the car.
As posted above, in this situation good idea to do a test that verifies the valves & rings hold pressure. Usually that is done w/a simple compression test. But when there’s a question if the valves and pistons might be bumping into each other, a better method is to test one or more cylinders by setting the crank/valves at the top of the compression stroke, then pressurizing w/compressed air and measuring how quickly the pressure drops.