I'm surprised no one has mentioned this one yet. Maybe someone has and I missed it.
When Kirk wakes up in the hospital on Earth (the scene where McCoy tells him "You were only a little bit dead"), look at the big bio-readout display panel on the wall behind McCoy. In the upper-right hand corner, you'll see some numbers and the name of the physician the hospital has assigned to oversee Kirk's progress: "Dr. Boyce".
Dr. Phillip Boyce was chief medical officer on the Primeverse Enterprise
under Captain Pike. (And was always my favorite character from "The Cage".)
I was disappointed by this movie overall, but the endless parade of subtle callouts like this one were much appreciated all the same.