(1) From what I think is the most problematic to least problematic.
a- Choosing a piece that is too hard for the student.
It's hard for a lot of teachers, especially newer ones to properly gauge the difficulty of a piece, due to these pieces being extremely easy at their level. This instant problem for lessons as the student will now become frustrated due to the difficulty of the piece. Some might start to feel boredom due to the little amount of progress in learning the assigned piece of music.
b- Choosing a piece that is boring for the student.
Everyone has their own musical tastes. Of course it's good to encourage students to learn a broad range of works. However, consistently disregarding the student's interests can make them begin to dislike learning the instrument.
c- Choosing a piece that is too easy for the student.
I feel this is the least detrimental to lessons as the students will at least have the facility to learn the piece. And thus a teacher will have a better understanding of the student's strength and assign a more appropriate piece.
(2) in list form in no particular order.
It's indeed very important for students to grow technically and musically, and to broaden their taste in music, but at the same time it is also our(I think it is)job to ensure that the student enjoys learning the instrument as this is what will encourage them to continue learning the instrument. Thus I think its important to assign them something they WANT to play along with those that they might not be as completely fond with.
1. musical taste
2. the overarching goal of the student and how the pieces I choose help bring them closer to that goal
3. technical ability and needs
4. musical ability and needs
5. their hand span
6. the season
7. their personality and whether or not a certain piece of music will be compatible with that personality
8. age