I don't know how many people are going to be able to discuss challenges across types of settings, because not many of us have been to multiple settings (though there might be a few). I also strongly suggest looking at past threads on the Psych Jobs Wiki for this, as I know it's been discussed there.
My short list (and you can PM me if you'd like): the difficulty of getting a lab going (physical setup, navigating new IRB, etc.), trying to keep research productive while likely doing at least one (probably more) course preps, figuring out all the little stuff that everyone else seems to know (e.g., policies for getting money to pay participants, other purchasing stuff, booking rooms for meetings), and trying to figure out how you fit into the department climate, which involves getting a handle on department politics. Every department has it's nuances--the people who get listened to, the people who are mostly ignored, the friendships and collaborations across the departments, opinions and perspectives on training and teaching, etc. I spent a lot of time listening my first year.