I'm going to separate this into two sections. Engine and interior/body.
Engine,
-The key would sometimes get stuck in the start position, this caused the starter to get overworked and eventually gave out.
-the steering wheel became loose, which made it hard to keep the car strait.
-Carburetor Problems! ha that is the only thing that actually went wrong with the car, ever since I got it it seemed impossible to set the carburetor correctly. She either didn't start on the first few turns or she didn't stop when you turned the key off. It also needed adjusting in the winter months.
Interior/Body.
-the door handles are a bit weak and seem to break easily, don't try to open the door when its locked
-the manual roll windows fall of their tracks and start to not roll up strait.
I have owned many vehicles and I have been under the hood of all of them. But I couldn't even tell you what the transmission looks like under the Tercel.
This car took a beating like I have never been able to give before, it was my fishing/hunting/mud-bogging car, there is simply no easy way to damage the car by hitting rocks or bottoming out, it has a perfectly placed front support beam that covers most of the engine and all of the oil pan.
In general its the biggest beater I have ever owned, its rusted and looks like it should be crushed, but even now that I have taken the insurance off to insure my truck I still don't have what it take to sell it.
I paid $300 for it and spent about $200 in repairs/oil/filter over its life with me.
Your car sounds like mine (I wrote the review just about same time as yours; mine review about it mentions its rusting out). The key spring busted so I learned to pull key back from Start to On. The driver door window glass came off its mechanism, I got in there and fixed it, and greased up the mechanism (why it busted, too hard cranking). The plastic part of door handle broke, I asked the mechanic about it, he said I could probably fix it myself cheaper, so I did. Once the driver side door was getting hard to open, I figured worn metal, so got in there with the factory manual (apparently written by well-intentioned person who hadn't actually done it, as I found only way to adjust the thing was apparently in factory before installation!), so I wedged a piece of metal in there, held in by paper clip wire (solved the problem and has worked since!). Yep, low power acceleration, and hard start below 10 degrees F (cause weak automatic choke). My previous car I'd replaced with manual choke I'd "made" myself using hints from someone's article, but this one I hadn't the spare part to fool around with (in case I messed up), so instead installed a coolant heater, and plug in car (extension cord on a timer) for frigid nights (really helps). Had some welding work done (guys in garages tend to place lift supports in places where it eventually pops open the bottoms of the rocker panels). Despite all the little things that need fixing on an old car, it has been rather remarkably reliable, but is rusting out on bottom.