Flags - in this instance 'wanes' is better. Fall is too sharp.
Pitfalls for a teacher - not either snare or trap, rather more to do with the act of teaching and controlling the class.
An uphill climb may well be treacherous but no pitfalls or treachery (committed by a person!)
Pitfalls - not of or in the law. Problems, deficiencies, delays, lack of competence are some of the matters you may come across in law but you are on the wrong track entirely with your thoughts on pitfall for this.
Student or Learner