jpsmith is right, dont study for failures, study for how things are supposed to be. There are some failures that are more common but studying to find them isnt the way to get a good education. If you want to be a good service tech, learn everything equally so you can handle everything equally.
Now I will sort of answer your question. The most common problems I find when working on the cooling side of the business are, incorrect charge (over charge or under charge) and other refrigeration cycle problems (obstructions, bad txv's and the like). If you understand the refrigeration cycle inside and out (literally) and the symptoms to each problem, you will be fine Also electrical issues, whether its a electrical component failure or an electrical issue that caused a component failure, you have to know electrical circuitry theory. The other big one is air flow.
If you study all areas you will be prepared. Yes there are certain things that are more common than others but every single system is different so you will never know what your getting into. Everything in a system can fail.
I respect that you want to be as prepared for the field as you can be, but nothing will really prepare you for the field better than being there. So just work hard on the basics and be prepared for the next half of your training, the in-the-field work.
The only true knowledge is the pursuit of knowledge