1. Numerous server and network issues (hit detection, latency spikes, poor connections, etc). No online game will be perfect, but for a game that is supposedly running on dedicated servers, it is astonishing that there are so many issues in this regard.
2. Parties get separated in games and players get put on opposite teams.
3. When in a party, players in the party are often unable to do anything in the postgame lobby (change weapons, leave, anything) because their screens are frozen black and remain that way until the next game starts.
4. Oftentimes it will take players anywhere from thirty seconds to a full two minutes to spawn into a game once it starts, leaving the other team ample time to run to their spots and dig in. You do get the unintentionally funny bonus of spectating your teammates that are lucky enough to spawn in, running around without weapons.
5. You can glitch out of the map in Point Du Hoc, an issue that Sledgehammer acknowledged when the game first came out but has yet to fix.
There are plenty of others but those are the biggest and most gamebreaking ones. It'll be a great game whenever they finally decide to fix this stuff (don't hold your breath), but right now if you're going to play it you're going to have to deal with some frustrations unrelated to actual gameplay.
EDIT: Should specify I'm playing the XB1 version of the game.