NOTE: The voluntary Nissan service campaign has ended. Long ago.
Way back when, Nissan had a campaign on all 84-89 300ZXs in the USA and would replace the injectors and some other associated components free of charge. If this wasn't done on your car, you should replace the fuel lines and injector seals. If you're unsure whether your car has been done yet, call any dealer with your VIN handy and they will probably look it up for you. If you don't know, you should probably do it, or do it again.

The early 300ZXs' injectors have a habit of leaking around the seam where they are pressed together. If they are not changed once they start to leak, your car will burn. Since this is not good, you will want to change your injectors once they start to leak. "But how will I know when/if they leak?", you ask. You will smell it, trust me. Anytime you smell gas in your car, check around the injectors and fuel rail, as this is where virtually all leaks start. It is a good idea to carry a fire extinguisher in your car, just in case. If your car catches on fire, unless you are really lucky, or near a fire station, it will be a complete loss.

It's not really hard to change the injectors, just takes some time. Here is how you do it:

1. Buy the new injectors. They usually run around $30-40 each (Unless you buy Nissan ones which are $100 a pop), and of course you need six. It's also a good idea to replace the pressure regulator now. I've been told that when it goes bad, it can take the air flow meter($502!!) with it. I don't see how this could happen, but it did on mine. It's semi-pricey at $130, but good insurance. I highly advise it. Buy the gasket that goes between the two halves of the intake manifold. It costs ~$5 at a Nissan dealer. You will also need a few feet of high quality 5/16 feul line. Don't skimp on the hose, the best stuff you can buy won't cost more than $2/foot. Do not, under any circumstances use cheap "no name" brand hose from Auto Bone, Western Auto, or somewhere like that. They buy the cheapest stuff they can find. I would reccomend you use Goodyear hose exclusively for this job, as some of the lines are not accessable without semi-major dissassembly. Also get some good quality hose clamps, locking ones are ideal. I would also reccomend that you change the fuel filter during this proccess. You will also need a set of injector o-rings. There two on each injector, one large and one small. These are the o-rings that seal the injectors to the intake manifold.
2. Relieve the pressure in the system by letting the car idle after unplugging the fuel pump. It will die in a few seconds from a lack of fuel.
3. Remove the upper half of the intake manifold, this is not as bad as it sounds. Unplug/disconnect everything on top of the engine, labelling if you need to, and work the manifold out through the rat's nest of wires, being carefull not to rip any of them out.
4. Immediately stuff some rags into the intake ports to prevent stuff from falling down there. This is bad if it happens. Your engine is meant to run on air and gas, not air, gas, chunks of gasket material, and a few stray nuts, bolts and washers. If anything should fall in there, be sure to remove it before re-assembly. If it is not retrievable, then you will have to, um, dissassemble the engine.
5. Unplug and unbolt all the injectors. Disconnect the three fuel lines that connect to the fuel rail. The entire injector rail will now lift up and out, injectors and all. Also be sure to remove the old injector o-rings.
6. Very carefully cut the injectors off the rail. Use the sharpest razor blade you can find. Try to avoid cutting/scratching the mating surface on the fuel rail, as this may cause leaks in the future. Blow out the feul rail to remove the ten years of crap that has built up inside, and any rubber shavings you may have missed.
7. The new injectors should have a short section of feul line already pressed onto them. The injectors are then pressed onto the rail. This sounds easy, but is very frustrating. It is an extremely tight fit, use a little gas as a lubricant and take your time. The quality of work is what determines how long these injectors will last. I always put a small hose clamp on this short section of line, closest to the fuel rail for extra insurance.
8. Put the new injector o-rings in place, the large one on the injector, the small one in the intake manifold, and set the fuel rail in place, being careful not to damage the injectors on the way in. Do not force anything into place.
9. If you have trouble getting those little spacer blocks to stay in place, tape them to the injector retaining rings in the appropriate orientation.
10. Torque the retaining rings down to the specified torque. This is something like 3 lbft, it is a VERY LOW TORQUE. Use a torque wrench, borrow one if you don't have one this sensetive. These parts are very sensetive, too tight or loose and air will leak around the injectors, which will require dissassembly to remedy.
11. Replace all fuel lines that are not easily accessable at this time. Also replace the fuel filter now.
12. Scrape away the stuck on gasket material from the mating surface of the two manifold halves. Bu sure it is clean enough to provide a good seal for the new gasket.
13. Replace the upper half of the intake manifold and re-attach everything you disconnected, making sure you removed the rags you stuck in there, and making sure the red rings on the gasket are facing downwards. Re-connect everything you disconnected, not forgetting the fuel pump.
14. turn the ignition on and let the car sit for a few seconds until the fuel pump cuts off, this means the feul lines have reached operating pressure. Start the engine, it will be hard to keep it running at first due to all the air in the fuel lines, but should be fine in less than a minute.
15. Carry around a fire extinguisher for a few days to make sure there are no leaks under the hood. It is a good idea to carry one around all the time.