So you want to buy a 300ZX. There a are some things that you should know to look out for, just like with any other car. Of course, check all the things that apply to all cars, look for rust, accident damage, bad body work if it has been wrecked, basic maintenance, etc. Maintenance records are good, but a car that doesn't have any records isn't necessarily one to avoid. If there are maintenance records/receipts/whatever, look at them and try to find the name/address of a/the previous owner. Give them a call and ask them about it, why they sold it, was it a lemon, did they have any freak problems, etc. I did this with all the cars I looked at when I got the 85, and both the people I found were pretty nice and helpful in general, I guess because they didn't care, they weren't trying to get rid of the car! This applies of course, if you're getting it from a dealer or from someone who bought it used themselves. Here are the specific things you should look for when considering a 300ZX:

1. Check to see that the vin on the dash, vin plate, model plate, and the vin stamped into the firewall match.
2. It is not uncommon for a car's owner to tell you it's, say, an 84 when it's really an 85. The 10th digit in the vin designates the model year of the car, E is for 84, F for 85, G for 86, H for 87, J for 88, and K for 89.
3. Before you buy the car, make sure that you see it first thing in the morning, when the engine is completely cooled down. Warm engines can hide starting problems, worn parts, weak batteries, etc.
4. Look under the car. See if the the front “frame rails” are bent, caved in, or whatever. This is indication of a light accident, maybe tapping a curb or something. If this is the case, have the alignment checked to make that there is sufficient adjustability to keep the alignment in spec. If a car has been wrecked, you should not automatically exclude it from consideration, it will probably be cheaper than an unwrecked one, and if it's been fixed competently, it's not that big of a deal.
5. If there are no records of the timing belt being changed recently, or if they look suspicious, change it/have it changed immediately after you buy the car.
6. Check to see if the injector work has been done on the car, and if it's suffered an engine fire. Fire will be obvious, look to see if the insulation on the underside of the hood is melted along with some wires. If the injector work has been done already, there will be a good many nice, shiny new parts on the engine and the injectors connectors will be spliced into the wiring harness. If it hasn't been done, make an appointment to have it done after you buy the car.
7. Look to see if the glass is all the same. Check in the corner of the windows, if the glass is not the same all around, it may be evidence of a wreck. Or it may mean that the car was broken into and the stereo was stolen.
8. If you take the car on a test drive, take it through a brushless car wash. The high pressure water will expose any leaks. Leaks are not uncommon where the t-tops, door glass, and roof meet, and they are very annoying as water drips in your lap and the seat may get wet. Leaks are also often found around the rear side windows(on the side of the car, right behind the door) They are not usually bad, but mostly leave drip marks on the inside of the windows. To fix this, that big piece of rear trim that the seat belt goes through must be removed so you can get at the two screws that hold the outside trim on. The window is held in by that annoying black, sticky, tape-like sealant. Push the window out and replace the sealant.
9. The only real common place for rust are in the back, at the bottom of the spare tire well, and on the left, right above the muffler, under the tool kit. Neither are serious, but if there is rust there, stop it now, especially at the bottom of the spare tire well, if it rusts through, it'll be a pain.
10. When you're test-driving the car, swerve violently and abuse the brakes. Also accelerate full throttle and watch for smoke in the mirror. If the wheel shimmies when you brake, plan on replacing the rotors, a ball joint, steering linkage, getting an alignment, or something along those lines. If you can get the wheels off the car, put two lug nuts on without the wheel and grab the rotor and attempt to rip it off the car. If you feel any looseness, something needs to be replaced. And, of course, if the rotor comes off in your hand, leave immediately and don't buy that car.
11. Look at the tread on the rear tires. It's most likely worn more on the inside edge than on the outside. This happens on all 300ZXs. Step back a few feet and stand behind the car, inline with the side. Look at the excessive negative camber that the rear wheels have, relative to the fronts. If the tires are worn very unevenly, plan on relatively short tire life, depending on your driving. Hard driving wears the tires on the inside faster that the outer edge, “normal” driving wears the tires fairly evenly.
12. Know what you want the car for. If you want performance and/or plan on modifying it in the future, a turbo is a must. If you plan on lowering the car with stiffer springs, plan on fixing the rear camber because when 300ZXs are lowered, the negative camber in the rear get ridiculous. Motorsport Auto sells a nice kit that's all worked out to give you either +1 or +1.5 degrees of camber in the rear. Any competent race shop would probably install the springs and the camber-fix-kit at the same time and align it for you for a (relatively)nominal charge.
13. Take off the oil filler cap and run your finger around the underside of the rocker arm cover. It should, of course, be very smooth and free of any particles suspended in the oil. If it's black, no big deal, it's just time for an oil change. Check the filter too, if it's a generic one, be a little wary. It may indicate that the owner doesn't do any work on the car himself. This is not necessarily bad, but cheap parts make for trouble later.
14. If you can, check the engine, transmission, and differential mounts to see if they've been separated. If they are, it won't cause a problem, just odd clunking noises. It's just another thing that may need to be fixed and is not that uncommon in all Zs.
15. Another sign of a previous wreck is the air conditioning condenser. Look under the front bumper up at the radiator. It's hidden way up there, almost parallel to the ground. The one in front is the a/c condenser, the radiator is right behind it. the condenser has a habit of warping in light front end boo-boos. It should be perfectly flat and straight. It will still work fine if it's warped, it just may indicate an earlier accident.
16. Remove the air filter with a 10mm nut driver and examine it. It should be fairly clean on the outside, and better be perfectly spotless on the engine side. Be very wary if it's dusty on the engine side.
17. With the car idling, go to the back and smell the exhaust. Any bad smells usually indicate a slight tuning problem. Also listen for any regular misfire or not-complete-fire. This may indicate ignition stuff that's worn.
18. If you take your time and wait for that one good deal you'll have a car that'll last for many years to come, don't rush too much.

Now that you know what you look for when looking around, you need to find some cars to look at. Here are the classifieds.