From a Concours Owners Group page I grabbed the following. It follows the list of all the positives of the bike. These are more for checking and using as "price negotiating tools"
Concours Owners Group - Mostly Biased Review of Concours
Many owners do their own maintenance. Basically that means oil changes and valve adjustments. There are other duties but those are the big two. The valvetrain has screw adjusters so no shims or removing of the cams are neccessary. Lots of engines out there, of all model years, with over 100,000 miles. Some over 200,000. Gene Kinzell has over 300,000 miles on his '87. An immaculate bike with high mileage has probably been pampered by its owner.
That said, the 1986 Concours had problems with soft valves suffering "tuliping" (the valve edges rolling into a cupped shape). If worried, a leakdown test will reveal it. There are camshafts (all model years) that show scuffing and pitting of the lobes but I know of no engines self destructing because of it. General opinion is that it's a result of Kawasaki's casting and plating methods and the stress of one cam lobe operating two valves, not rider abuse. Mine (1995) have some pits and it hasn't affected performance any.
The junction/fuse box (J-Box) can develop cracks at some solders joint causing electrical bugs but that is easily repaired with a touch of a hot soldering iron. The petcock has been known to leak and cause the carb float bowls to overfill. The petcock trouble is a haphazard thing. Some fail, some never do. They can either be repaired or replaced with a manual tap. Adding an inline fuel filter keeps the float bowls and the needles clean and seating fully.
For a "first look" inspection on a used bike check for leaks. By your left foot peg look for oily sludge inside the bottom fairing pan. That's oil residue from a leaky clutch rod or shift shaft seal. Both easy to repair. The water pump is in that general area too. Its seal could leak and is replaceable but not as easy a fix as the other two. Not as easy but not that hard either. Sniff around for antifreeze. Coolant leaks are usually a loose hose clamp or old O-Ring. Again, an easy fix. Move back to the final drive and driveshaft. These are a little harder to fix but not terminal. Leaks are always good bargaining points. These leaks aren't common but on a bike 5 years or older they could appear. All these things are considered normal wear and tear and not defects. The Concours' engine has no terminal faults and will give good reliable service for years if cared for properly. The aftermarket makes some performance goodies for the engine if you want them. You can even transplant Ninja 1000R cams and carbs and return her to former sportbike glory.
My gas mileage is about 43 mpg with 235 miles before hitting reserve, but I'm not obsessed with squeezing all the gas I can into the tank. Nor am I careful about getting every mile out of the tank either. (your mileage may vary) Rust inside the fuel tank has been a problem for some. Check the tanks for rust inside the filler neck and bubbled paint around the lower edges caused by fuel leaking through pinholes. Don't poke these bubbles or you may have to pay for a new tank. Also look for signs of internal tank coating treatment. Could be the seller already had rust. You may end up replacing that tank later. A new tank is expensive. Regular use of Gas Dryers and keeping the airspace inside to a minimum helps prevent this corrosion.
Tipovers happen. When the 600 lb. Connie tips over the footpegs and/or their mounting can crack. Get in close and look for stress wrinkles and cracks. Run your hands under the saddlebags for gouges or cracks. If she has been dropped and the bags were on, the mounting "antlers" could have cracked too. Feel behind them for cracks, wrinkles, or bends. They will feel loose and wiggly. They're designed to do that. Take the bags were off, check them for cracks or scratches, and look at the mufflers for scratches and dents. Look at them from the rear. They should be even. Also check the rear footpeg mounting brackets for cracks. The exhaust cans are attached to them and could be damaged in a fall.
Check that the inner fairing panels are fairly equally spaced from the tank. If there isn't any clearance on one side or the other the fairing mounting bracket may be bent or just sloppy Kawasaki assembly. Try to lift the upper fairing. If it moves it's probably a loose Main Fairing Bolt. (http://www.mindspring.com/~gbyoung2/misc/frame/fairbolt.jpg
) A loose bolt couls saw through the mounting tab. Look for cracks above the front running lights where the plastic is narrowest. Besides checking the mirrors for scratches and cracked glass, grab them and gently work the swivel mechanism looking for slop. Careful, it's fragile. Check the fuel tank and look for dents where the fairing may have pushed into it. Remove the side covers and seat and look for damaged paint on the chassis and engine from spilled battery acid.
Check the fork sliders for oily film. That means new fork seals. Check the brake pads for thickness. Ignore any tire cupping. The causes of that are in dispute and range from tire pressures to braking technique, to brand of tire, to loose steering head bearings. The cupping doesn't necessarily indicate any terminal problem. Lots of different bikes do it.
This should be enough to give you a general idea of the bike's condition. Anything more involved will require a mechanic's eye. Have one look the bike over before handing over any cash. Sort of a grim picture, huh? This is a worst case scenario and not typical of every used Concours. Most of it is normal wear-n-tear stuff, common on any used bike. The Conc is a reliable, workhorse of a bike. Tough. The kind you can ride all day and "put away wet" without worry. Spend a few bucks to have her professionally inspected just to be safe.