I have been thinking about buying an 86 coupe from down the road from me and I was wondering what some common or weird problems may be. It was a beater, but I am not worried about looks at the moment, just worrying about if it will run. I want to know some of the problems that the AE86 & AE92 owners have had.

common issues... not in all cars... but many

headlight switch - can get flaky requiring tapping to get it to work
heater control "TEMP" slide gets very difficult to move, and can cause the whole assembly to break
rear diff, or axle bearing howl
early models has issues with door pulls (cups)



lots more... but that is off the top of my head

Oil leaks from valve covers, distributor seals (inner and outer), rear mail seals, I even had a leaky dipstick tube O ring lol. Keep in mind these cars are pushing 30. I'll 31 and I know a lot of my parts don't work like they used to....

I think I I think I have all of the above symptoms...

I wouldn't say "Common or Odd Problems", more like normal wear&tear, and aged parts.
You will have to repair and/or replace everything.
If you have the time, money, and resources. Go for it! It's quite an adventure.
If you don't have these things, please reconsider. You'll just end up hacking up the chassis and eventually passing on a half-finished project to someone else. (I lost count of how many times I've witnessed this.. )

Thanks, everyone.