New... the engine should have about 150 psi compression. (cold engine, open throttle) BUT... anything over 135 psi is acceptable. If it has been sitting for a long time (put away for the winter) start, and run the engine for 10 or 15 seconds. There could be extra oil down in the crankcase, and it will give you a false high reading.
There aren't any special things to watch for... but if you are paying premium price... I always recommend water testing it, to make sure everything works. A jetski can run fine on the trailer... but it can be a big hunk of crap once it hits the water. (won't rev up, over heats, cavitation to the point where it won't move, or takes on water fast enough to sink)