Been wondering what the updates contain for the new Halo: MCC? Well look no further because 343i does have info on their patch notes for these, 343i Halo Blog, this link will take you to all info regarding the Halo: MCC.
Overall it has had a drastic improvement since day one release. When the game first launched their were multiple problems with its Match Making progress as well as almost everything in the game had something wrong. Including problems with campaign, achievements, settings and other stuff. Some people had a bucket full of issues while others only had a few (like me, thank god). But so far with all the updates it has been working out and getting better and better.
Team Halo 2: Anniversary (Ranked)
Halo Championship Series ( Halo 2A)
Team Slayer (Halo 1-3)
Big Team Battle (Halo 1-4)
Halo 2 classic
SWAT (Halo 2/A & 4)