The biggest change immediately noticeable is the granary; it no longer has anything to do with your food supply after your population increases (that's now the aqueduct) so the old instinct of get that first and fast also no longer applies. There are also no internal limiters to city population, so if you don't specifically tell a city not to grow then they'll go way faster than your tech and production can keep them sedated for happiness.
The AIs are often extremely schizophrenic. They'll declare war with one or more people, then, if they take one city or their units get destroyed, they'll turn around and ask for peace. Either way a couple dozen turns later they'll do the exact same tactic all over again. I'm like, dude, if you're going to declare war then you should mean it and go for the throat.
They're also often insane as to what reasons they give for going to war. "They think you're settling too many cities too fast". Really!? No Really!? Of course I am. It's called a force multiplier, and the earlier the better. There are also no warnings signs that someone who has complained once 30 turns ago is suddenly going to declare war (sounds like they just got really bitter over time about their original complaint, even though there's nothing feasible to be done about it).
I suspect one of the computer players were cheating in my last game. He only had half a dozen cities, bought out almost every single city state in the game (no easy feat, considering it takes about 60 influence (~500 gold) just to make someone an ally, much less keep them as an ally), was making around 300 gold per turn, and had several thousand stocked up. And this was only on 'normal' ("Prince") difficulty.
Some city state types are also extremely over-powered. Spend about 250 gold every 30 turns and all of your cities get a bonus of food, so the more cities you own the bigger the effect, and somehow their single city can supply all of them. There are similar affects with some of the other city state types.
Toward the end of the game the delay between turns (as the computers made their moves) started bogging down my machine, of which there were only 8 players and 16 city states. By no means do I have a weak machine; 3GHz quad-core, multi-GB GPU, 4GB of DDR3 memory, etc. But the graphics would freeze up and I couldn't do anything for something like 5-10 seconds. The graphics also started acting up. Units four tiles away from a city would suddenly start attacking it, or pikemen would start attacking units two tiles away (both legal moves, yet visually incorrect).
My biggest complaint, though, was the scarcity of strategic resources on 'normal' distribution. With 5 cities covering a significant portion of the continent I got all the way up to the industrial age and discovered that there was no oil (a multiple resource required to build almost any advanced units; strategic resources occur in counts of 1 to 6 per tile, and units will 'consume' one of those counts for the lifetime that it exists) in my area or anywhere near it. In fact I would have had to go two cities into my neighbor to find any. This meant no planes and no tanks, the former of which was the only thing which could have saved me from the cheating AI. And of course no one wants to give up these kinds of resources, so it's not like I could barter for it.