The time that I was most afraid as a CFI was when I was flying with this guy named Mike. I think that Mike had a learning disability or something because after 10 hours or so, he was nowhere being able to maintain heading and altitude at the same time.
We were landing after one lesson and as we rolled out, all of a sudden he stomped down on the right rudder pedal for absolutely no reason. The airplane almost departed the runway, but I managed to regain control. It would have been highly embarassing to groundloop a C150. Not to mention that my life flashed before my eyes. After that, since I had already put in my notice, I turned him over to the FBO owner.
I also had another situation with an instrument student in which we had a audio panel failure. The intercom worked between me and my student, but unknown to us, we were transmitting on a hot mic on the #2 comm. We figured out what was happening and cut the #2 radio off but we were still transmitting on it (sounds impossible I know, but it happened). We eventually got ATC to find an empty freq for the #2 comm and we used the #1 for the approach and landing.