what to watch out for when buying a crappy old frame to upgrade/refurb?

Don't sweat the seatpost; you can get a spacer to adapt almost any size to a smaller one.

Most bikes I've seen from the era you mention have a compatible BB shell with modern BBs even though the actual parts are different. How to tell for sure? I don't know; consult sheldonbrown.com.

The rear spacing will be 120 for five or ultra six, or 126mm for six or ultra seven (ultra narrow chain/sprockets). Modern road wheels are 130. The rear wheel will be a freewheel design which means you will bend the axle unless you go to a modern 130mm freehub or upgrade some other way. You can buy a 27" wheel with modern hub like I did for my Schwinn World Sport or just go with a 700C wheelset which is only 8mm smaller rim dia. Or go singlespeed which will eliminate the massive rear axle overhang and allow the old hub to work. Steel spacing is easy to change.

My suntour rear derailleur seems to work fine with an 8-speed cassette but takes a little while to go into first or eighth.

Bring a can of oil when shopping. Grease will be dried up, if you find one of those gems which has been sitting after having been ridden once or twice, like so many are. It's better to drip some oil onto the wheel, BB, and steering bearings than nothing at all and the bearings are almost sure not to be sealed.

Last, there's a lot of [censored] out there. Some of the bikes don't have hook edge rims, for example. You'll pump up to full PSI, then there will be a loud bang. Most of the better bikes will have aluminum rims (except American Schwinns and possibly others). Chrome steel rims brake very poorly in the rain.

Or the frame will flex so bad from pedalling the brakes will momentarily drag when you accelerate away from a stop.