From what i've heard, the biggest remaining issues are:
-laggy co-op campaign over Live
-some achievements aren't unlocking
This is just what i've heard, since I don't have an Xbone yet. MCC could have been the game that got me to buy one, but not after hearing about how broken it's been.
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Both those issues are resolved and one of them like any peer to peer relies on the hosts connection and your connection to them. If your ISP isn't up to scratch there is nothing 343 can do as far as I am aware as it still uses Bungie's netcode. CE-3
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Overall, connection issues have bern resolved, some bugs still are a problem though. Plus in multiplayer everyone quits early so it's a pain to find a good game of multiplayer. However with the campaigns i'd say that's worth $60 by itself with no multiplayer.