New 1996 Galant ES owner. Problems.

Well, yesterday I bought a 96 Galant ES with only 79k on it for $3200. According to Edmunds I got a very good price. However, there's some problems.... I test drove the vehicle and everything seemed fine. To be honest, my dad and I were looking at a lot of vehicles and just didn't have a lot of time to spend test driving.

I have what appears to be two (maybe 3?) separate problems. On the way home from purchasing the vehicle from the lot, not 2 miles down the road, the car started smoking a bit from the right front (coming out the right wheel well). It did this lightly til I got home. It appeared to be a white smoke. Also the car was idling poorly and roughly at stoplights. I drove the car hard and for lots of miles later and the smoking did not reappear.

Additionally I have what appears to be a transmission problem. The car shifts strong up through the gears, and back down, until it is down shifting from 2nd to 1st, where the car has a jerk. Seems like the opposite of a slip. Perhaps the torque converter is catching hard? Remedy?

Can you all help me diagnose these problems? I got a warranty with the car so hopefully if any of these are major problems I can get them taken care of, but I'm also afraid that they may claim these were pre-existing problems, and not fix them. Any course of action I can take if I believe that the dealer hid problems he knew about? Thanks all.

look for any signs of rubbing from wheels tyres and pulleys that might cause smoke. as for the gearbox if there is any signs of problems take it back cos if it goes wrong your knackered, stay clear off any car with box problems unless you are prepared to spend some time money and effort