It's probably not even worth mentioning since it's fairly obvious, but for me to complete my rear case replacement, I had to transfer three bumper-like brackets from the side edges of the old case. These brackets help hold the screen in place so they are pretty important. Six screws total. Two of the brackets were on the left and one on the right.

Additionally, there are three mesh screens behind the holes for the two microphones and the bottom speaker that weren't on my replacement case. For optimal sound performance, it's probably prudent to move these to the new case as well.