How effective is the army AI if given specific objectives?

I've noticed that I can command armies to take objective areas, but how should this be utilized?

When I mark objectives should I mark all territories that I want my army to take during a time period, or should I pick a few "lynchpin" points deeper in enemy territory? If I do the latter, will my army spread out and take a wider front or do they automatically bee-line to the objective territories with a disregard for for other factors?

From my experience, the AI is just horrible, so don't use it on a theater level. If the scale of operations is small enough, you should micromanage each unit. This is, of course, not feasible for larger (or even medium) fronts; for those, you should use "lynchpin" points, as a rule of thumb, one for each corps (if you're still managing at that level) or 3 for each army. See this excerpt from the wiki on it:

To make things work well with AI automation you need to use the preparation stance a few weeks before declaring war in order to let the AI organize the forces as it sees fit. Don't try to organize things neatly with a corps in each province, it will never agree with you. It likes to shift units around a lot. Also try to set as few objectives as possible. More objectives mean more confusion. Never ever set a corps more than a single objective, and don't give more than two or three to an army. Setting objectives to corps isn't great though. It's nearly as bad as micromanaging everything yourself in terms of the attention it requires and you constantly have to deal with the fact that automated corps do not cooperate with each other (most of the time they ignore each other).

I think you'll probably find the entire page this was from to be of use, so here it is: http://www.hoi3wiki.com/Military_AI_and_human_control