Adding to points above (all very good ones by the way!)
Automatic transmission: I know DPI sells a new reproduction transmission governor, typically a failure of it would make it shift very strangely. If you see RPM's not at all match speed in a very strange manner (as an example, redline at 2 MPH dropping to idle at 5 MPH from a stop light), transmission reauires a rebuild and valve body usually also needs work. I say this with two cars' worth of experience in failures, the second of which is my DeLorean. (We tried to avoid cleaning the valve body at the time as the weather was amazing and I was horribly impatient. Still worth it.) It feels like what you would expect to see if you were in a stickshift and somebody was dicking with the clutch. It's a very odd experience, but the engine responds normally throughout (remember that when the car finally "catches", RPM's will drop due to load, not to it being an engine problem).
Frame rust, that car flipper's frame was around the left tow hook as I spotted before, but another area to be VERY careful of is the suspension mounts around the engine. Sometimes rust will be patched insufficiently down below only for it to creep up above. I have seen some nasty rust in that area, holes in the frame even, and it supposedly "drives just fine". For now, anyways...
If there's one thing visits to DPI have taught me, it's how DeLoreans met their end in ways that could have been prevented. On one total loss, the top of the shock tower had a rust hole big enough for two or three fingers to fit through on one, DPI told the guy he would not work on it unless he was able to repair it. Didn't even make it to the highway before busting the shock absorber through the frame at that railroad crossing, I think even through the fiberglass as well. Combine that with undercarriage damage like mad from scraping, and a "daily driver" insurance value, it was a goner. (In the owner's defense however, that particular crossing from DPI to I-76 is one hell of a bump, even the big rigs go over it at 2 MPH, and I myself hate it in ANY car.)
Seat covers are available readily, just to clarify that part, upholstery shops can easily do it and will. Vendors work with you on fabric selection and color. Other parts, guess I haven't been here long enough to see a reproduction interior part, but that one's on my radar to tackle under Raccin. It's why Raccin is here, if no one else will do it, I will. Don't expect any timely manner though, I just finished moving yesterday and now need to find where I put all my projects. Not to mention 2-3 years and only now tangible results on one smaller item.
LCA, I have damaged ones if you want pics of what a bent-out-of-shape one looks like. I have a lot of failed parts from my own car I'm sitting on waiting for someone to need it, occasionally I find someone and sell it to them. This is in that category, but it's also good for reference pics.
Fuel system, you haven't run into this yet, but wait till you see a carb or an EFI! These guys can be religious about it, but not always (I'm DPI brand EFI now and agnostic
), sometimes coming along with engine swaps (I think the DeLorean was a rare one to use the mess that is K-Jet), but those have dedicated sub-forums somewhere here for them.