My god, I guess my 2003 TJ is considered "old". Seems all relative though, in that it does not seem to be a 20+ year old vehicle. But I just realized all 5 of my vehicles are at least 10 years old, with the newest being my 2013 Ridgeline.
But, anyway, Wranglers, yeah, rust is the thing to look for on TJs for sure. Like has been mentioned earlier, oil leaks are a thing. I have a piece of cardboard under my rear main seal, even though it was just replaced a few years ago. Honestly I think it's better for that seal to be driven daily, I think mine leaks because the Jeep will sit for days and days without being driven. We really should sell that thing, but my wife has owned it for 17 years and has an emotional attachment to it, so it stays around more for sentimentality than anything.