I baught a rebuilt engine and have 120 psi on the 2 passenger side cylinders and have 0 pis on the two drivers side cylinders. Do you think the person that rebuilt it messed something up?

i assume you checked the valves are set properly

Even a really bad engine will have 'some' compression. As mentioned check the valve lash.

usually a valve stuck open for some reason

How sure are you that you did the test correctly? Having two dead on the same side sounds suspicious. Did you get the tester threaded all the way into the hole? How did the engine sound when you were cranking it over, before you took the plugs out? With two dead holes, I would expect a sound kind of like "RR-RR-..-..-RR-RR-..-..", while an engine with compression in all four would sound much more even. "RR-RR-RR-RR".

You might want to visually check as much of the interface between head and cylinder as you can, and try to wiggle any head studs you can get a finger on. Gaps in the interface or a wiggling stud means the head isn't on correctly.

If the engine isn't yet in the car a lot of this checking becomes easier.

Double-check the valve lash, as was already stated. If the adjusters are screwed all the way out and you still have some clearance, the pushrod may not be seated in the lifter cup inside the motor. You have to remove the rocker arms to correct that.

If the valve tips (the part the rocker arm presses on) are closer to the head on a couple of valves even when the rocker arms aren't pushing them, you may have a dropped seat or two.

If you can't find any cause for it from the outside of the engine, you'll probably wind up having to pop at least one head off to have a look around.

--DD