Well in no particular order a few specific problems I think the AI has:
1)Failure to recognise it's a bad move to found a city that is not on the coast, but has several sea tiles in its radius.
2)Even allowing for chopping being toned down in 1.61 the AI still keeps far too many forests.
3)All AIs refuse outright to trade techs only they own, even when this is detrimental to them (e.g. when they could trade it to two other civs for a tech from each).
4)AIs leave far too many units simply sitting in cities while relatively small numbers of enemy troops are in their land. This is particularly bad with navies, where the AI will leave a dozen ships sitting in a city while a couple of mine they could easily destroy pillage their improvements. Similarly the AI does not remove ships or great people from cities in imminent danger of being captured.
5)After the initial attack the AI tends to just send units into enemy territory as they are built rather than building up a powerful force, making it much easier to wipe them out since they can be picked off one at a time.
6)AI builds far too many workshops, especially given they rarely run State Property.
7)General poor usage of Great People, particularly in the early stages where the AI tends to use them for golden ages. They would be far better used as super specialists, academies, for discovering techs etc at that stage.
8)AI fails to recognise that coastal cities which are icebound do not have access to the ocean, and will then build ships which can never leave the city.
There are also a few specific leaders which play badly as part of their personality. Tokuwaga for instance invariably cripples himself due to his isolationist approach and objection to open borders.