Find out whether the AMM has been replaced lately. That's a real trouble item on the 83-84 240's.
As with all 240s, look for rust. This car will likely have the most trouble in the rear wheel wells under the spare tire, and the back ends of the rocker panels at the front of the rear wheel arch. The entire floor is also subject to rust- the seam at the outer edge of the floor panel where it meets the rocker panel is the worst spot. It can really be anywhere in the floors however- it's very important that you fully assess that and BE PREPARED TO SAY "NO DEAL" if the floors are shot. A car this price should have very little rust. There are lots of 240s for sale with bad floors for a lot less money- here in CT they ALL rust out, but at least they're cheap: see www.bargainnews.com and search for Volvo, $1-$1000 and you'll see what I mean.
The rear hatch is also subject to rust in both the window frame and the bottom edge; also look closely at the lower edge of both big side windows. All of these spots are not fun to fix.
If that's all ok, you can move on to electricals- the car should have had the wiring harness replaced by now, not just repaired, and there should not be any crumbling wiring anywhere under the hood. That includes the battery cables. They're pretty easy to replace but not cheap from Volvo.
Look around for oil leaks going down the right side of the engine, as well as transmission fluid leaks from the cooler lines and back by the driveshaft.
Look for evidence of coolant leaks, particularly on the top of the waterpump, right side of the engine. Try to get a look at the condition of the exhaust and brakes.
The car is always going to need SOMETHING- just try to make it as good a deal for yourself as you can.
Good luck!
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Rob Bareiss, New London CT ::: 86 244DL, 87 244DL, 88 744GLE, 91 244: 808K total