At first glance (I'm still in my first game of EU3), I think the AI is okay. It has the level you can expect from a strategy game, but it's not stellar, and it still needs a lot of tweaking and bug-fixing.
Here are some of the AI problems I stumbled across. Please keep in mind that this is my first game, so I may miss something obvious, or misunderstand something.
- The AI doesn't colonize aggressively. I could completely claim both coastlines of the real-world U.S. without much competition, despite the fact that one or two European countries had had 50 years of time to claim land there before I even learned about the New World, and despite the fact that dozens of other nations learned about the unclaimed land at the same time as I did. Very valuable provinces (gold mines, for example), easy to take and maintain because of peaceful natives, lie unclaimed for decades.
- When the AI does colonize, it often does so in a seemingly erratic way. It's not uncommon to see AI colonies simply die. In my game, one AI had colonized a string three provinces on the south east African coast, which all simply perished some years later (so the AI simply wasted about 200 ducats). Trinidad has been colonized twice, and both colonies died soon later. It's kind of realistic actually, but still stupid and wouldn't be too hard for an AI to prevent or circumvent.
- I haven't seen colonial conquest in my game. I don't think the AI ever decides "Let's conquer these savages across the ocean and take their riches", as many colonial powers of in our history did. The AI doesn't seem to actively pursue colonial conquest strategies.
- The AI is very weak at evaluating peace offers. It rates provinces according to their economical power, but it seems totally oblivious to their strategical importance. For example, I had Austria repeatedly offering me the "Steiermark" province, which I didn't even want - it was a poor and underdeveloped province, so the AI thought it wouldn't hurt much to give it away. What the AI didn't see was that by giving away Steiermark, it would cut its capital off from all its other provinces, including the harbors, which would make further colonization attempts impossible.
- The AI is similarly clueless to the strategical importance of other countries' provinces. In 1453, Burgundy starts with its capital cut off from its coast provinces, so it can't colonize. Burgundy has a huge army, and a huge fleet, so it has the potential of becoming a substantial power in the New World. It just needs to take one province from France, or (if it doesn't want to anger France) two provinces from puny Lorraine. It would be easy for Burgundy to conquer puny Lorraine, but it never tries to. As a result, the huge Burgundian fleet sits motionless at Holland's coast for decades, costing maintenance.
- Even when the AI is getting conquered, it sometimes just sits in one province (with good defensive modifiers) and waits for the player to come to it. If I don't, I can occupy all its other provinces, and force it into vassalization in the peace treaty, although I would actually *lose* if I engaged it in combat. This seems to happen especially when I park a huge army directly adjacent to the province with the AI's huge army. The AI simply freezes because it doesn't want to give up its good defensive position, and I can lay siege on all their provinces undisturbed.
- In my game, I have a Portuguese fleet west of Florida which hasn't moved for decades. The Portuguese apparently forgot about it. It just sits there, costing maintenance, and never ever moves.
- The AI doesn't use the tactical advantages of its armies. For example, with a fast army, you can overtake a fleeing opponent, await them at their destination, battle them again (you are very likely to win again), and repeat this until the enemy army is gone. It's a very obvious strategy, but I don't see the AI applying it.
- Also, the AI can easily be lead into ambushes. The way the armies flee is very predictable so you can easily direct a fleeing enemy army right in front of your guns/pikes. The AI doesn't seem to be able to do this. Actually, the AI seems rather clueless about the strategical situation in a war, and only concerned with the immediate vicinity of its armies when moving them. (But I'd need more testing to check this).
- The AI doesn't think ahead in diplomacy. I've repeatedly seen an AI granting another country military access, only to declare war on it soon after.
- There are bugs in Diplomacy which seem to lead to the AI wasting its resources - like Funj (in Sudan) repeatedly trying to get a royal marriage with Sweden, which IIRC isn't allowed because they don't share the same religion. Even if it is allowed, it's utterly pointless. I've also more than a hundred attempts (I'm not exaggerating) of AIs to form an alliance with Sweden, all of them failed, because Sweden is already allied with Castilia and Aragon.
All in all, I think the AI still has a lot of issues - however, this has to be expected from a game as complex as EU3, especially so short after release. I've heard that Paradox is very dedicated to improving its games with patches, even long after release, so I guess we'll see some AI improvements in the future.
And actually, at least for my first game, the game is so much fun that the AI hickups don't especially bother me. It's something I'd like to see improved upon in the future, and which will be very important for long-term replayability, but truth to be told, the game is very enjoyable as it is.