"We are going to be working our way through the car to make it a solid reliable driver for him." -- I'm not sure this is a realistic goal, or even an attainable feat. But I'm excited to watch you try!
I don't know a bunch about the 80, but I own and regularly do battle with a '87 5000 Quattro. The 5 cylinder engine is reasonably reliable, but nothing else is. It's possible the 80 isn't as bad as the 5000, but there's a short summary of my ownership (copied from a totally different post):
When I bought it and drove it home, it smelled like burning hydraulic fluid because the steering rack was dumping hydraulic fluid on the exhaust. The warning display was alternating between coolant overtemp (it wasn't), low hydraulic fluid (it was), and brakes (eh, who knows?).
That was a few years ago, and the Audi and I have had some great battles. My weapons have been perseverance, an inscrutable Bentley manual and eBay parts from Estonia.
I managed to fix the cold start issues by installing the missing fuse for the CIS computer. Point mine.
The odometer stopped at 184,199. I took it apart, unwedged it and it restuck at 185,299. Point Audi.
The after-run relay for the electric cooling fan melted. I replaced it, and the replacement melted and drained my battery. Point Audi.
I fixed the coolant temperature warning by replacing the multi-malfunction sensor in the thermostat housing. Point mine.
Oh man, the GM-sourced Cadillac climate control. It mostly worked, but did what it wanted to do, with occasional random responses to button-pushes. But then the heater core started dripping on my feet, and I replaced it. I fixed the leak, but the servos and levers and springs and magic for the ducting have never worked correctly since. Tie?
I fixed the acceleration hesitation by replacing one of the electric valves for the CIS. When I removed the electrical connector, fuel came out. Of the electrical connector. Point mine, but it gets a nod for creativity.
And then the clutch failed in a weird way. I couldn't get it in gear reliably. I replaced the clutch master and slave cylinders. That did not fix the problem. Against my better judgment, I replaced the clutch. The pressure plate was just plain worn out. Plenty of life left in the disc. While I had the transmission out, I replaced the steering rack. This was less than $200 in parts from rock auto, but geeze was that a lot of work. Many points to me.
A relay of uncertain function started clicking while driving and after driving. I removed it. After doing so, the driver side door chime stopped working, which is a huge relief. Unfortunately, the power windows stay powered until you open and close one of the non-driver doors, which means every time I get out, I have to open and close another door to keep the battery from dying. I think the Audi won that one.
Things I've never even tried to fix: the hydraulic accumulator for the brake assist (really, it has one of these!) was busted from the beginning and I've never even tried. The brake assist works fine as long as there's hydraulic pressure. It won't work if you use the brakes a lot or if the engine isn't running.
The right-rear brake caliper sticks. I ordered a replacement, and the part number was actually the left rear. So I installed that one and tried to order a left, hoping it would fit on the right. No left exists. I disassembled the caliper, cleaned the piston, honed the bore and it stopped sticking for awhile. Just last week I did it again.
In the time I was winter-commuting in it, I have never actually gotten stuck anywhere but my own house, which is really decent of it. I have discovered plenty of pools of fluid underneath it when leaving work, but it always got me home. There were lots of days, however, that for one reason or another it did not actually manage to leave my driveway. Or the time it left my driveway, but the clutch stopped working on my street, and I limped it back. If I were relying on it exclusively to get me to work, I'd be unemployed.