Engine
Normally, what one should do is check all the fluid levels to make sure they are of the correct level before you start up the motor. Look at how clean the oil and coolant are. Oil should be a light tan color and feel smooth between your fingertips. If it's not, don’t be fooled by the salesman offering you a free service and oil change before you take delivery. The crude needs to be taken out before any more damage is done.
Check the coolant in the expansion reservoir on the driver’s side of the engine bay. Not only should it be spot on the level, but take the cap off and make sure there is no oil floating in the fluid. RB26's have been known to crack their cylinder heads, and the only sign is oil contamination in the coolant. Any sign of contamination is bad news and its best you move on to look for another car.
After looking around the engine bay for any obvious signs of abuse, misuse, lack of care, trails of leaking fluids and so on, go in and turn the ignition key but don't start. Follow .S K A G E E.'s step and go ahead and check if all the check and warning lights light up. As he has mentioned, all the lights should be up and if it is not, someone has tampered with it. If it all lights up, start the engine and it should all go away. If any of them are still lit up, you have a problem. Don't take the salesman's word that it will be fixed after an ECU reset.
Listen to the engine note. It shouldn't have any nasty noises and the motor should be nice and quiet, rustling a bit at idle rather than clanking and knocking. There can be a little tapping from the valve clearances if they haven't been shimmed recently and you can also hear the injectors clicking at idle but nothing too excessive.
Next, check the mileage. At 100 to 120,000km the engine will need to be ‘freshened up’. It will probably need new bottom-end bearings and suchlike. This means that if you’re looking at a car with this sort of mileage and the job hasn’t been done yet, you’re likely to have a large bill in the near possible future. There are plenty of GT-R’s that are running with more kilometers than this but that depends really on how well an owner takes care of his car over the years.
Crankshafts can be a weak point if the motor has been over-revved. Even occasionally letting the engine rev to more than 7800rpm is not healthy but anything below that should be fine. Unfortunately, no one can tell whether an engine has been over-revved until something lets go but if you feel that the motor is very rough at the higher revs, you should look at choosing another car. Straight Six-cylinder motors have perfect primary balance so they should be smooth all around the rev counter. Any coarseness should indicate that the crank is not as straight as it should be.
Turbo’s can also be a problem if it’s the standard ceramic ones particularly if it has had the boost wound up. As .S K A G E E. has mentioned, the stock ceramic turbines are quite fragile. The problem with the ceramic wheels in the stock turbos tend to shear off or fly apart when the boost is wound up above 1.0 bar, which is why most people would rebuild them with steel internals to stop the problem from recurring. Ceramic fins will offer slightly quicker spool time compared to the steel one’s but are more fragile when boost is turned up.
Once the motor is up to temperature, you can check the oil pressure by raising the rev to 4000rpm and checking the oil pressure gauge in the MFD (Multi-Function Display) or just look in the meter cluster in front of your steering wheel underneath the RPM gauge. I can't remember if the stock MFD has the pressure guage, but the Nismo MFD version 2 should have it. It should read 4.0 bar of pressure steadily. Because of the way the gauge is calibrated, you cannot check the pressure with the engine just idling. However, using this 4k rpm at 4 bar rule should prove if the pressure is good enough.