A thorough inspection must include at minimum a compression test, and that is a bare minimum. You should ideally have a cylinder leakdown test (CLT) done as well. Diesels run at around 20:1 compression -- compression loss means they become difficult or impossible to start in cold weather.  A compression test or CLT is pointless, with the head gasket blown.  If the head gasket is blown, there is an excellent chance the head is warped and will need to be machined before the new gasket is installed.

You will also need to have a mechanic assess if the diesel injection pump is functioning properly. If it isn't, the general cost to rebuild is in the area of $800-1500.   Proceed with caution when looking at a used diesel. Only buy a car with a favourable (read: frequent oil changes), documented maintenance history available. Diesel operating principles may seem (relatively speaking) simple. Repairing them is neither simple, nor inexpensive.

Buying a Used 760T Diesel.  [Tips from Andre Lam] The problem with the I-6 D24 (and worse on the D24T) is that the oil from the pump enters the head at one end of the engine, and has to cascade down to the other end. This causes severe engine wear during short runs. Ones the oil is hot and flowing freely, this becomes pretty much a non-issue. If VW had re-designed the engine to put the oil to both the front AND the rear of the engine then we might not have so many unhappy previous Volvo diesel engine owners. Heck, I got better life from the proven POS '81 Olds Delta 88 than either of the engines in my '84 760TD. It seems that the VS and Audi engines were not as problematic since they were 4 or 5 cylinders, and therefore the oil delivery was sufficient. The other issue is the turbo charger in the 7x0 and 9x0 series diesels, this further added stress to the engine. In their favor, the D24T was an absolute dream to drive on the highway. The engine pulled strongly, and was much more pleasant than a base B23 in a car that size and weight. Off the line with the slush box things were a bit hairy at intersections. The car seemed to wait a second or three for the turbo to spool, then pow... the car started to pull briskly. This car had true turbo lag. Without the turbo... its a dog, with the turbo... very brisk. Noise was very well subdued as well. The engine ran very smoothly. I really liked the car (if only the engine would last). If driven all day long, then the car will last and last. If you drive it shorter distances, be prepared for an early engine death experience. The cold start was an other item that needed to be checked on regularly. If it was not functioning right, it could also contribute significantly to an early death. The "wonderful" change over in Diesel fuel a few years ago was also a real joy as upwards of %25 of all diesel cars on the road had their pump die shortly after the cutover. Since the pump IS the whole fuel system (pump and timing device) it is a complex beast that costs about $700 to have overhauled, re-installed and adjusted. They normally last about 100,000 miles, so that is not bad, but thanks to the fuel, lots of people got "burned."
Would I purchase an other diesel car in the USA. No way. For the last decade regular gas was CHEAPER than diesel, and sometimes I could get premium fuel for less than diesel fuel.  Mileage was only so-so. My '84 760TD (w/ 4 speed automatic) got about 17 MPG around town and about 28 highway. I can easily beat that with either my mom's 95 850 (4 speed automatic), and definitely better in my '93 850 (5 speed stick). Here in the USA it is also hard to find good diesel mechanics. I took mine to the VW dealer hoping that at least they would have experience ha! They declared the car in perfect health. Two weeks later my engine is toast with below par compression. Rebuilds are possible, but here again a good mechanic shop is hard to come by. In Europe where diesel is sort of reasonably priced, gasoline is 4 times the USA cost, gas stations are much more likely to also have diesel fuel, then my arguments can easily be beaten with simple economics. The NEW direct injection diesel engines from VW in the 850 are supposed to be really excellent. They run quieter (not really a problem in the 7x0/9x0, but certainly so in the 2x0), don't suffer from turbo lag, and get far superior mielage, and don't smoke up the neighborhood when you take off.

D24 Diesel Valve Clearance Procedure.  [Query:]  How do I set the valve clearance on the D24?  [Response: Dimitar]
cool engine down completely.
1) rotate engine that 1st cylinder is on T.D.C. (both cams are up 1st cyl. and mark on bellhouse aligned to flywheel mark)
2) measure valve clearance for that cylinder
3) if too small obtain thinner plate and exchange the old one with that one.
4) do it until clearance is 0.20 +- 0.05 mm cold for in and 0.40+-0.05mm for out valve.
5) rotate crankshaft for next firing cylinder adjustment (1,5,3,6,2,4 order).
6) repeat procedure
7) rotate engine twice and check everything again
8) do it every 20,000 km or so.
9) replace with new one valve cover gasket.

Be sure to point down plate side with number on it.  You will need pliers for valve plate and valve lifter tool. It is the same tools and same procedure as for VW or any Audi diesel.