The game was rushed. (some proof inside)
I had at least 2 instances where cut scenes did not play or are simply missing.
The introduction of the french commander outside New York and the scene that plays after you catch Miriam during a Homestead mission.
Many of the bugs mentioned in the article and in other posts i've experienced on my own as well.
There is a mission in AC3 where you have to chase a man around the streets of New York and tackle him. He always runs in a circle, throws money, is just ever so slightly slower than you, goes through alleys and turns corners consistently (which is a major issue because now that you don't hold X to climb you will repeatedly attach to the environment), and one of the 100% sync objectives is to not push civilians. TL;DR it is an extremely poor designed mission that just asks for too much from a completionist.
Also take into a consideration a similar mission where you have to chase one of the main protagonists from the docks. You can't push civilians, you have to stay 50m within range of the target, you can't traverse the surrounding environment because at 60m you lose sync, 4 lines of guards block your path and if you get knocked down once you lose sync, if you use smoke bombs there is a limited area of effect, if you don't have the smoke bombs pre-equipped before the mission starts you have to hold R2 to access them repeatedly, assassin recruits move far slower and close the distance from a longer range making them pointless, etc. TL;DR, bad design.
There are countless missions that either have stupid optional objectives for 100% sync or are just poorly designed.
Many aspects of gameplay have been streamlined or redesigned for no reason and strip away more freedom, or make your actions more cumbersome.
You don't need 7 different assassin recruit abilities. All of them are useless outside of the optional missions you must use them in.
Rope darts are pointless outside of the frontier.
Trip mines are useless in every scenario.
You can only assign 4 items instead of 8 with diagonal d-pad presses.
Quite a few of the standard assassin devices from the previous 3 games are absent and they were actually useful. Blueprints for the assassin order lost in time...
For every step forward AC3 takes, it also takes two backwards. Good game regardless but insanely flawed.