Hoi3 is a very difficult game to project an AI for. The amount of variables is huge and there is no penality for overextension like in EU. Also, even very little mistake can lead to crushing defeats against human players, as MP games showed so many times.
Some things are already quite decent, like the air war, the sub warfare and the management of land fronts against a player with and equal or inferior force that distributes his forces evenly. If the front moves slowly
In my opinion some the biggest flaws of the hoi3 AI are:
_Inability of having a focused build up strategy (Hoi3 really discourage dispersive builds)
_Too many garrisons even where not needed, so the forces are too spread out and many divisions are very vulnerable. The AI should be able to distinguish cases in which a port garrison is not needed, like when there is naval superiority, or when an inland reaction force is better than divisions in the ports. If the choice is to garrison the coast, than it is needed more than some divisions in the ports, but also garrisons in the adiacent provinces and something inland.
_More in general, (related to the previous point) the ability to prioritize some theatre and leave others undefended (too dispersive)
_Also related with the previous, the ability of chosing which theatre to prioritize (Germany commits way to much forces in Norway everytime)
_The ability forming a sparehead for offensive warfare and countering the enemy sparhead in defensive warfare. As said, the AI alwais work with an evenly spread force, which is very ineffective.
_The ability of keeping the forces focused on a target. The AI management of units is a mess. always strategic reployments everywhere (which, btw, creates a lot of supply problems), troops that take a province and than retreat instead of pushing to next one. I've often seen Germany stopping it's adavance on at the gates of Moscow for no reason, with the Soviet defence already shattered.
_Awful management of HQs, alwais out of range.
_Inability of breaking well built defensive lines, even with a crushing superiority in numbers/quality, the AI can't make sacrificing attacks, for example to cross a river. It just stands there.
_while newly built units have a quite OKish composition (with exeptions), the AI can't rework existing units compositions.
_I don't even want to talk about the naval warfare. I know it is difficult, but at least a proper fleet conposition and bigger fleets would be nice. And the AI probably needs to be a little more conservative.