My previous post was about how you may find something, along with how you can do it. However I'd like to add to both sides of this discussion. Prior to finding this site, my old methodology was - leave no stone unturned. And I'll admit, I did check facebook. Getting a divorce had not been discussed and I was trying to figure out what was happening to my life. I call it human nature.
On the one hand, her facebook digs against me, pics out partying when she should be with the kids and communications with OM are not useful to my case and only hurt knowing my kids were second to her, my friends may have seen this stuff and that she had friended OM for longer that I knew. In fact, as Bart has pointed out before, this info will become a hindrance, technically and emotionally. No doubt about that. My STBX's facebook info scrub ended with useless data, new wounds and time wasted. My wheels were spinning but I was going nowhere. And really, who cares?
On the other hand, how would one know if there's anything useful or not, w/o checking. I did gain one bit of info that was concerning, regarding OM's facebook page, pertaining to my children's safety. But this only led me to get a backround check (eVerify 7 day free trial). Which led me to call the courts in question. Which could have all been done without facebook.
I'd leave it at - Checking facebook will come at a cost. Ask yourself, what info am I looking for that will help my case? (note that facebook is a bunch of bs and it's not filled with silver bullets) Unless you have valid reasons like contempt or neglect or adultury (if it matters), I suggest not to check. If you think you have good reason to check, do it once and do not get caught up. It sounds like you don't think you will get caught up...but be warned, you probably will.
FWIW, my new methodology is more along the lines of - don't go looking for info because this is how life after should be. If you directly receive concerning info, look into it.