My final winter it happened multiple times a week. One horrid snow after the other and one time I spent 3 days in a row at the airport, couldn't get home. Ohare is a major airport that has so many connecting flights from it. Cargo was a much better fit until a stupid barge hit a bridge at 3am but that wasn't all the time.
Now this is prior to online check-in but I'm sure it still works similarly. I could tell who were premier level travelers, business travelers, the elite, VIPs. Did anything not to bump the 'important' people' 'cause I'd trade one problem for a new LOUD problem.
For special needs people I'd first look at the notes of disability. A generalization but my blind passengers generally wanted an end seat, hard for them to climb over other passengers. I found deaf passengers normally picked window seats and often took photo's during the flight out the windows. For kids UMs I'd look for a seat as far up as I could and on an end so the attendant would see them. We usually had a cute badge on them especially the younger ones to ID them as a UM. I'd also look for a Mom-ish aged woman to be in the middle seat next to the UM and I tried never to bump one family member traveling together. I found myself when I had kids flying as UMs, Moms traveling with children tended to take my kids under their wing when boarding etc. One time the same family came home again with them and my Sister was so surprised this 'stranger' in Ohio airport knew my kids names, lol.
I also tried to bump a passenger that had not yet checked into that flight, then the gate agent had to deal with the bump not me. The gate agent-when bumping passengers was happening-always made an announcement for volunteer bumps. Volunteers at time usually got a credit for that flight and a voucher for $100-400 for their next flight. Many years ago my family took a bump at MCO. We were overnighted at the hotel at the airport and went out on the next morning flight. We walked with $1600.00 in vouchers for our next Disney vacation. So often the person I first bumped wasn't the one left at the gate. I know it is cold but you kinda get numb to passenger fits even when they are in the right. When it came to UMs or Medical Transport passengers, if a flight was going they were going to be on it. I hated to make that call to their parents and the receiving person of the UMs that their kids were stranded at Ohare due to a lost connecting leg flight and would be staying overnight. Parents and worse grandparents tended to freak and I understood the panic. Nicer phone call, flight cancelled so they are now inbound on Flt. XXX instead arriving at xxx. It is also why when I sent my kids to Ohio, Cali or Florida it was always on a Non-Stop flight.