One thing I dislike is that DH is still very inflexible when it comes to the AI responsiveness and that it's still very event-driven. You can say many bad things about HOI3's AI, but it reacts to both historical and unhistorical situations as best as it can. If it suxx at doing sth, then it will suxx at this no matter what and if it is capable of doing sth, then it will be capable even if you do ahistorical things. In HOI2, the AI is scripted to react to historical and some semi-historical situations, but outside of that, it's hopeless. For example, when I attack Manchukuo and Japan as the SU, in some cases they will not even cover the frontline properly and will not use their airforce against me, which will still be stuck in China, while the HOI3's AI doesn't have problems like that. It doesn't meant that it will not fail - on the contrary, it fails often, but at least it knows what to do because of the generic nature of its scripts.
Another problem is the lack of any logistical system. HOI3's system has some problems and design flaws, but in most cases it works quite well and it really limits your actions in many areas.