I have not been a fan of the first two "reboot" (or "Kelvin timeline") Star Trek movies. They're not bad movies, but they are bad Star Trek. The original Star Trek--in fact, Star Trek in all its iterations--was about interactions between the characters. The original series (TOS) was built on the interactions between Kirk, Spock, and McCoy. In the first two Kelvin Timeline films, Kirk and Spock were the main characters and the others, including McCoy, were just there to take up space.
Fortunately, that has changed in Star Trek: Beyond. McCoy became a full partner in this movie, which can only help the franchise. Additionally, there were many homages to previous movies and TV series (I'd mention them, but don't want to include spoilers).
There was an dedication/acknowledgement of Leonard Nimoy's death. Know what choked me up, though? "To Anton".