What are the biggest differences transitioning from undergrad to grad school?
This may be closed as "primarily opinion based" (especially the second part), but I'll take a whack at it.


  What is the biggest thing to overcome/accomplish during your first semester [as] a graduate student? 


Your first 1-2 years is likely taking classes. So, the biggest thing is passing those classes. This should be achievable (though a lot of work), so I'll list also two secondary goals: making friends, and finding an advisor (though this may be a bit early to line up an advisor; every university has a different process).


  Looking back, what is something you wish you would have done differently?


Stayed in my office more. I tended to work on my own at home; while I learned a lot, grad school would have been more fun if I had made more friends and done some of the work collaboratively.