Here are some things I noticed about the AI, through my tests, and observing others.
1. The AI tends to go after easy targets. If you leave a VP city open, they go for it over a heavily defended area. Sometimes this is good, other times it leaves them open to be surrounded and destroyed. Players can set traps for the AI, easily cornering them and destroying them by manipulating their goal towards undefended 'important' areas.
2. I believe the AI prioritizes provinces on a number of factors, VP level, depot, harbour, city level, etc. It seems the 'better' the city, the more the AI wants it.
3. The AI does not seem to remove embedded commanders from brigade command. For example, Holmes and Bonham will most likely be brigade commanders the rest of the game, even though they would better be served as divisional commanders. I believe the AI 'can' and sometimes possibly 'does' (although I have not seen it directly) remove them from command, but, for the most part keeps those assigned to brigades (and most likely divisions and HQs) in their assignments. So, beware if you assign scenarios to have lots of Brigadiers assigned to Brigades (I have modded Brigadiers into the stack, but not directly in command of a brigade, giving the AI and Player the option to do so).
4. The AI does sometimes attach leaders to silly units. One was Holmes (whom has been modded not to be embedded to his brigade) attached to a cavalry regiment who was just about to enter a 'death ride' behind enemy lines. A waste of even a poor leader. I personally have modded out leaders from being attached to cavalry regiments to stop the AI from attaching and killing off their command structure.