Let me start by saying I've never been divorced; however, as a high school teacher I've seen plenty of it, enough to know how devastating it can be on everyone.
One issue that impacts socialization as well as self-esteem and even time management/academic issues is divided custody. Staying in two homes, leaving a book bag in a car they won't be in for another 4 days, getting a permission slip signed for the right parent for the right custody day, communication in all areas--it's always stressful and sometimes embarrassing to have to make it all work when you're 16 years old and just want to be "normal."
Nothing is worse to watch from the outside than parents using their children as sounding boards for their grievances against each other. It nearly always breaks their hearts at first, but soon it blossoms into disrespect. Older kids, especially, understand that adults should not be doing such things--especially to their kids. What a position to be in, hearing awful things about someone they love. The dynamics of that are complicated and, I suspect, long-lasting.
The worst for me to watch was kids whose parent(s) began pursuing other relationships and left their kids behind, so to speak. Can't tell you how many broken hearts and broken promises I saw. Parents who virtually abdicated one family to assume a new one. "My dad said I can't go to his apartment anymore because he has a girlfriend and he thinks I'd be uncomfortable." Really? You'd rather your kid felt abandoned and unloved than a little uncomfortable? This scenario is about the parent's comfort level and convenience, not the child's.
On a brighter note, I have seen a few things done well by divorced parents. Some will come together to parent/teacher conferences; some will work together on a fundraising effort or class project; some will communicate with me independently but include the other in the e-mail.
It's not much, given the significant negative issues, but it is encouraging when parents put their kids first, as they should.