Basically, what the others have said. In addition, look inside the door jambs, under the hood, etc., looking not ONLY for overspray, but for "masking lines". This is where they ran their masking tape. The paint they sprayed will be a thick layer along this line and it's harder to fix than simple overspray.
Look around (and at) the headlights (if the headlights were involved, were they aligned?) and openings for the grill. Look VERY carefully at your windshield, even though it wasn't involved in the repairs (things happen in shops). Check your tires and suspension for overspray. Look INSIDE the wheel well of the fender they did and compare it with the original on the other side.
As IndigoGTI said, "orange peel" is texture in the paint's surface. The texture of the new paint (if any) should be the same as that of the original paint. And as bunker said, the parts they painted should look EXACTLY like the original paint. Look at it from numerous angles to make sure the color/metallic effect matches and that there aren't buffer marks. Ask them about what glazes they might have used that might be covering such marks. And ask when it'll be safe to wax the repainted areas.
Make sure they didn't get sloppy on the underside of the hood (look under the insulation if you have it). Make sure your HVAC intake area isn't filled with bodyshop debris (and cycle through heat/vent/AC/defrost to make sure your ducts aren't filled with it). Look for those masking lines I mentioned and overspray and missing/incorrect fasteners (and for fasteners that were incorrectly coated with paint). Check the hinges, latch, and related springs. Be sure the hood release works properly and that the hood closes as it should. Make sure your washer lines/nozzles are as they should be. If you have a rubber airdam under the bumper, check it out.
You're looking for ANYTHING that isn't perfect, or like the car was originally. REALLY (!) take your time. There's always a tendency to miss something until the first time you detail, and then it's usually too late (although a GOOD shop will stand behind its work). And yes, LEAVE IT THERE if you're not completely satisfied.