In my experience, perhaps one or more of the following:
Incorrectly identifying the types of energy involved in a situation, e.g. not counting a type of energy which is present.
Using energy conservation to solve a problem where energy is not conserved—such as when friction is considered.
Incorrectly identifying the system when it comes to using energy conservation or the work-energy theorem.
Lack of a solid understanding of earlier foundational concepts which come back to haunt them with e. con., e.g. objects in free-fall where a launched object is concerned.
Basic mistakes that are made in plenty of other types of problems as well:
Dropping negative signs, especially in a derivation (happens to the best of us).
Incorrectly deriving the final equation to solve for an unknown variable where energy conservation or the work-energy theorem is concerned (yay algebra—check your work by making sure your units work out if you have trouble with this).
Not so much mistakes as a lack of understanding that will be fixed with practice:
- Not being able to identify sources of error where energy conservation is used, such as recognizing where energy is lost in reality that is not considered in a basic physics problem (production of sound, air resistance, heat)
Just off the top of my head :)