Engine burns oil (about 1 Qt per 700 miles)
The vinyl seat upholstery is cracked and falling apart.
Air conditioning doesn't work (broken when I bought the car, was told it would cost around $300 to fix)
Air bag light is on (also on when I bought it, and would also apparently take $300 to fix)
Exhaust pipe rusted through between engine and muffler (95,000 miles).
Spark plugs became fouled at about 130,000 miles (at least 50,000 on that set of plugs)
Radiator corroded and slowly leaking (135,000 miles)
Clutch started slipping and was replaced around 110,000 miles.
Heater can't keep the cabin very warm when it's below about 10F/-12C (average winter around here).
As long as you check the oil and coolant levels, it's been more reliable than most lower-mileage (newer and older year) cars I've driven. The things that've failed on me are mainly because it's an old car, and the only preventative or routine maintenance I've ever done since buying it is change the oil and oil filter every few thousand miles. Rusting exhaust systems are fairly common in this area, with the snow and salt in the winter; spark plugs should at least be checked and gapped more often than 50,000 miles; and when they say to use distilled water when diluting antifreeze, there's a reason for it, and I ignored it; two people learned to drive a manual transmission on this car, and the clutch was near the end of it's life to begin with, so I'm not surprised it wore out (They're not cheap to replace, however. Definitely something to keep in mind).
Starts within two or three revolutions every time, even when it's so cold you can't shift because the transmission fluid's gelled up (I've always parked outside, and there's no engine block heater or heavy-duty battery or starter).
Performance is decent at slower speeds. Above 45 MPH the acceleration starts to drop off; while it can get to 85 on a long, flat road, that last 20 may take a few minutes. Definitely not for road trips, or busy highways.
The cabin is very loud when driving; there's probably no sound insulation, or if there is it's completely ineffective. I tend to wear earplugs or headphones when I'm driving more than a few minutes, or else I'll get a headache from it.
Handling is fairly good for a car this size and speed, although power steering would be helpful.
I wouldn't go offroading in it, but it'll handle a Minnesota winter just fine if you're in the cities. Although that would depend some on how good the snowplows are in your area; roads get plowed relatively quickly in my area, so it's rare that I have to drive in more than an inch of snow. The only time I've gotten stuck anywhere is when I intentionally drove into the 7" unplowed snow at my employer's parking lot to see how far I'd get (about ten feet), and a few minutes with a shovel got me out. Anti-lock brakes would be nice, but they're hardly necessary, and as I understand most Tercels don't have them anyways.
Avoid the vinyl seats. Once they start to crack, they go quickly, and I'm sure any vinyl this old will have cracks in it, or will very soon.
Don't pretend that you can fit people in the back seat. You can't. Not full grown adults with legs, at least. The front seats are fairly roomy, however. Trunk space is adequate, if you can fit your cargo through the smallish opening.
The engine's not too difficult to work on for oil and filter changes and such, although whoever positioned the oil filter exactly where it is has my undying hatred. You simply cannot fit a standard strap-type filter wrench in that space. You need one of those sockets that goes over the end of the filter and plugs into a ratchet, and even then it's a tight fit.