Now that the most glaring, fundamental issues have been kinda-sorta fixed, I keep noticing all the smaller issues that were overshadowed.
A big one for me is the lack of any postgame lobby. Previously in the series, after a game you'd go to the carnage report with the rest of the players from both teams. There was a lot of trash talk, sure, but it was also a chance to talk about the game with your teammates, offer some "good game"s if you played with decent folks, maybe even party up if you really enjoyed playing with them. Halo 3 took this a step further by rolling the entire session into the next matchmaking search after a few moments -- you had to quit back to the menu to leave the group.
But in MCC, when the game's over your party is disconnected from the session entirely and sent to the carnage report alone. If you were talking to your matchmade teammates (or opponents), that conversation gets cut off. And because there's no in-game indication of which players are talking, if you want to party up with somebody you enjoyed playing, you have to laboriously search through 3-15 players in the carnage report, sending messages to try and identify the right person (who's probably already in an unjoinable "Find a Game" screen anyway).
These aren't huge changes, but when coupled with stuff like the restrictions on team/proximity chat and the difficulty in accessing people's file shares, it puts a damper on the community spirit that flourished in previous games. Harder to talk to people, harder to party up, harder to share stuff, harder to find new friends. That's not what Halo has been about.
(Also, seems like adding in a postgame lobby that rolls into a new matchmaking session would help improve matchmaking times. If it's so hard for the game to find good matches in a timely manner, why disband the session and start from scratch after every game?)