This is what they call experience!! Think about how boring it would be if you didn't have any stories to tell your grandkids.
My experience is that most issues do come up early and then as things are resolved it will quiet down, although I have to admit I haven't had major issues with tenants destroying things.
I agree with @Mike Sattem, get the door fixed ASAP. I would call the police department and see if a police report was filed. What you don't want to do is accuse your tenants and then find out you are in the wrong. You also don't want to assume they are telling the truth if you have some evidence to the contrary.
Also, this is a good time for a display of leadership. Let the tenants know that you are not a pushover. You show it by keeping up with your responsibilities (cabinets, outlets, door) and holding the tenants accountable for keeping up theirs (not damaging the property, paying on time)
You can also evaluate the performance of your PM and if you feel you are getting a good value or not. If not, I wouldn't hesitate to let them know that they are not meeting your expectations. If they don't improve, get another PM.