The car does look nice. From the pictures. Frame seems to be in good shape. So does the interior and engine bay.
I would ask more about the front fascia and specifically why the passenger headlights don't look like they are sitting quite right to me. Some eyebrowing there, yes, but to me the pair looks like it is not secured properly, like maybe there is something going on with the housing assembly behind it. That part is this one:
http://store.delorean.com/p-6884-hea...g-assy-rh.aspx and while it is NLA at the moment, Ed in the UK mentioned he is having some made. His initial date was early January, so that might need some follow-up. Not all the spoiler and rockscreen fasteners are where they should be so maybe that's part of the same story. Ask about it.
Noticed both sides of the car are missing these:
http://store.delorean.com/p-10095-se...-exterior.aspx They aren't very expensive and are an easy cosmetic (and functional) improvement to keep the weather off the end of the seatbelt bolt.
Also missing the inside cover from the passenger door pull handle, here:
http://store.delorean.com/p-9912-gra...e-rh-grey.aspx You don't need the whole handle, just the cover. And you may not need it if it just fell off inside the door and is still in there somewhere.
There is also no belt on the A/C compressor. Assume this is for a reason and that the A/C does not work. Why it does not work is a mystery. Could be that it just needs a belt. That isn't too likely though and it could be reasonably expensive to get it all working again. That's a guess though and the biggest question mark about the car from the photos.
I would also ask about any history they have on the automatic transmission shift computer governor and specifically whether it has been rebuilt with modern electronics. I feel as though these computer boxes on the automatics all need to be updated. So not a matter of IF but WHEN. If it has not been done already then count on needing to do that on the car to be able to enjoy driving it.
You could ask about whether the auto trans fluid filter has ever been replaced and you might also ask about the fuel accumulator and whether it is new. That and any other records they have and can share on the car.
Yea, being cautious with BHCC is a good decision. They do have some okay cars for sale as well as some awful ones. Choose wisely as the old guy guarding the holy grail in the 3rd Indiana Jones movie liked to say