Hi and welcome.
The age the vehicles are now at means that accurate service history's may be scarce and this should not put you off. I would approach it in the same way that you would approach the purchase of any vehicle. At 170,000 miles it is just getting run in, the 80 is a tough old beast but even the toughest will suffer from abuse. 'The rear differential does not work'? I would guess he meant the differential lock assuming this GX has lockers? Assuming there are no obvious clouds of smoke/knocking/changes gear (manual or auto?) OK, then I do not worry too much about mechanicals, they can be purchased and bolted on job done. Next to the interior, good interior parts are getting scarce or the price is becoming ridiculous, so that can be a deal breaker, I went and looked at an 80 years ago and there was a generator bolted to the floor, oil all over the place and was listed as 'immaculate'! Re the leather seats, the 80 had options and they are often swapped over, for me in Spain they are a no no, so cloth for me. You need to way up your budget, does the car need new tyres, a set of four is not going to be cheap, also a good indicator is if the tyres on the same axle are the same brand, four different tyres tells me the car is being run on a shoe string.
The real issue for me is RUST and general bodywork. Unless you are good with a welder (I am not) then to repair properly is going to be expensive, the 80 suffers in particular around the steering box, panhard rod, and rear arches/inner arches, the tailgate is also quite common but is a bolt on job so not a problem. Depending on your budget and if the condition is poor this could break the bank. There are some mint examples about but they are not cheap, what are your plans? Keep it mint and stock, modify for off roading, lots of decisions to be made before purchase.
Add in the usual HPI checks and other pertinent documents and make your decision, good luck.
regards
Dave