Hi there!
There were a lot of them but some wasn't really hard to handle.
Here are some challenges I remember :)
1) Serfs
2) The rise of the middle class
The rise
of the middle class in the towns in the high to late medieval period is
one of the great moments in history where you can see reverberations
down to our present day.
3) Religion
Those in
charge of towns or castles always had to deal with the organized
Christian church in the medieval period. In the early period (500-1000)
the church had little real political power in most situation, but from
1000-1400 the situation changed radically, and power struggles between
the church and royal powers were common.
That's all I have and I hope it helps!
P.S. I just take that from my notebook.
Good luck with your Wold History class.