Well, I guess I know something about them since I have one
3. Rust. OK, all LBCs of the era suffer from it, but the Jensen-Healey has an even worse reputation than most. Look underneath the car at the floor pans, right behind the doors where the rear fender connects to the sill, and also the sills themselves. Due to some "interesting" ways of designing things, these spots rust very fast (mostly due to owners not keeping the weepholes cleaned out, which results in water just sitting in those crevices). The sill is a big concern because it's a major structural part of the car, and if it rusts badly there isn't much keeping the car from folding up. I would get down there with a magnet and whatever else you need to do to make sure that the metal is solid and not just "Bondo-ed" over.
Off the top of my head, those are the big things to look for. If it's really in as good of condition as you stated, it's a gem of a car and I wouldn't think twice before buying it. They are really easy to fix when things go wrong, and parts are not at all difficult to find (it sourced parts from several other British cars of the era, and I've never had trouble finding parts during my restoration).
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