For instance, if you stop at the red light and you release clutch while still in gear in manual transmission, the car would wobble and die. Of course you can start it up again, but what is the actual damage caused by such mistake?
While this isn't good for the car (obviously), it will not cause any irreparable damage. It's just a learning thing which you kick yourself in the butt for, but it's not going to cause the car any real harm.
Ok, thank you. But what is happening in the transmission when that happens?– winterFeb 7, 2015 at 18:34
Nothing. There is a bit of higher stress, but most of the abuse is taken in the engine, not the transmission. Some of it is taken up in the dampening springs in the clutch as well.– Pᴀᴜʟsᴛᴇʀ2 ♦Feb 7, 2015 at 18:36
what is the actual damage caused by such mistake?
tl;dr: Very minor wear on the clutch.
Assumptions: you're motionless, the engine is idling, the clutch pedal is on the floor and the gear level is selecting the wrong gear (I do this most commonly with third gear rather than second).
At the green light, you're ready to move on! You blip the throttle slightly and release pressure on the clutch pedal. Unfortunately, since you're in the wrong gear, the road has a significant torque advantage over your engine at this point. In first gear, the engine would be able to rotate the transmission and wheels fairly easily. In a higher gear, either the engine needs to put out significantly more torque (more throttle) or you'll need to feather / slip the clutch to keep the engine from stalling (slower clutch pedal).
What happens when you stall in high gear is something simpler: the spinning side of the clutch tries to get the motionless side of the clutch to start turning. This is a futile effort since the motionless side (connected to the transmission and the road) is not interested. As such, the spinning side rubs away in vain until the two sides firmly grip each other once again (i.e., the car stalls). This process is over quickly and, since it's at low revs, is very minor wear on your clutch.
Feathering / slipping the clutch, however, can lead to quite a bit of wear. The temptation in that case is to add lots of throttle and slowly move the clutch pedal. That leads to the horrible smell of burnt clutch. Don't do that.