The safety related comments are good ones.

Limiting my answer to problems in the air, I see a number of things all the time (not all with the same person):

- Moving the sticks too far. Even on a trainer, you don't need much stick travel.
- Not letting the plane fly. Get the plane to straight and level flight, and let the plane fly. A lot of guys seem to think they have to constantly be moving the sticks at all times.
- "pulseing" the controls. The controls are proportional, not on-off, like a home video game. So, apply a small control imput, and HOLD IT. I see a lot of guys who want to "jab" a large control movement for a short period of time, or pulse it to try to do something. It doesn't work very well (if at all). Looks really funny on elevator though.
- over banking turns. Kinda like overcontrolling. But even guys who do everything else right frequently want to see the wings really banked over before they think it's enough to turn. You really don't need much bank.
- being able to tell when the plane is and is not "straight and level" It comes with a little practice, but some people really have trouble with this one.
- related to the one above, being able to tell if the plane is climbing or diving in certain situations, such as a turn, or flying towards you. It's incredibly common for new pilots to dive everytime they fly towards themselves.