I often see vintage Jaeger-LeCoultre watches for much less expensive than I would expect. Should I be wary of the quality and movement of their older watches, or are they just less desirable than, say, a Rolex, Cartier, or Patek?
You should always be wary of movement quality, but no more so with Jaeger than with anyone else. They're less expensive not because the movements are inherently lower in quality; they're less expensive because rich idiots are willing to spend gobs of their ill-gotten filthy lucre on pissing contests with Rolex, Cartier, and Patek, attempting to outdo each other in conspicuous consumption. Those three brands (especially Rolex) cost more to collect vintage models for the same reason that the work of Damien Hirst is expensive: cult of personality, combined with taste-proof wealthy collectors.
You are aware, aren't you, that Jaeger LeCoultre actually made a lot of the movements Cartier and Patek have used over the years? Rolex, not so, but whatever else you can say about Rolex movements, they're not in any sense fine or particularly mechanically interesting — good, solid, and unobtrusively reliable is about the best you can say of their in-house production. If vintage Jaeger is more affordable, so much the better — collect them; at least you are not paying the Rich Moron Tax.