Thanks for asking, mostly I've played HOI1, a little of 2 and just recently started playing HOI3. So I'm not that experienced with it yet but here's my bit because changes would make me enjoy it and play HOI3 more:
1) Allow the Player to control the number (add and delete) and define the zones of Theatre HQs, which should also have an improved AI when handed control of them. Theatres ought to come up with a plan to achieve the objectives you assign to them and realistically assess their force needs when making requests.
2) Have separate Airforce HQs (that are more adept at using Aircraft inc Air Transports and Paras etc) and Navy HQs (esp with better AI Naval tactics etc) and perhaps have a Supreme Command HQ (that unassigned units are directly attached to when withdrawn from current organisation tree - also for a general reserve) above these two Air / Navy HQs and the Theatre HQs.
3) OOB GUI for both Units and Leaders that you can use to click to follow and find your Units and Leaders and as others have mentioned some way to see all attached Leaders or unassign all to make that quick and easier to micromangage. Leaders ought to be auto-assigned better according to traits and skill and experince levels and of course these should also be gained realistically during the game.
4) Better AI all round in terms of knowing how to match up against threats etc, defend in depth and to properly secure VP, resource rich and strategic Provinces. Stop the AI from fighting without continous fronts or abandoning fronts altogether. Reduce the strange activity (far flung invasions, unrequired Exp Forces that you can't block acceptance of while their home country is losing elsewhere) and the pacivity (no US D-Day, no real Pacific War, no British involvement in NA & ME) of AI controlled Countries.
5) MORE USEFUL SLIDERS - This has slightly been mentioned in this thread but this is my most important issue at the moment. Again the AI is crap at handling Trade in Deplomacy, but also IC in Prodution and Leadership in Intelligence. I would like to have the AI control these things but IMHO as others have said it just can't. Leadership is easy to just set as Normal because it seems more static and only needs to be checked occationally, but the IC sliders in the Production screen (GUI) need to be adjusted daily (at Midnight) for optimal results. I have to constantly manually pause the game at Midnight, but sometimes miss or accidentally "resume" after a pop-up & pause which is really annoying particularly when it means wasted IC!
I would like a "Pause at Midnight feature" for this reason unless the "AI Control" of these Sliders can be given setting objectives to attain. Or you could mark them similarly to locking them but that would maintain the level you wanted in say Upgrading but less for Supply if you have a large Stock pile. It would be good if there were two degrees of locking, hard lock and hold (like now - especially at zero) and a soft locking floating mark. That would mean the AI could manage not to waste IC or Leadership as actual levels of things change. I would also like to set the Trade objectives like this, indicate in the Diplomacy scean (GUI) just what and how much I want to trade with and for and have the AI try and achieve that, because this could ultimately manage your resourse requirements for you.
These sort of things would make it easier to play although I definately think HOI3 is better than the older versions.
I have a sixth point all of my own as far as I can see and it has to do with the vanishing of retreating units. Firstly I would like to see a message or pop-up when this happens and I understand it to mean that the land unit has surrendered but I don't believe it should happen in the case when there is still another Province available for the retreating unit to escape to but the one it was about to retreat to has just been captured. I find it too unrealistic & gamey in such cases. People have complained about ships and sub dying too quickly in sea battles and units not having a setting to stop them fighting to the death because it takes a lot to produce units to have them just so simply disappear in these situations. Having some sort of a stop attacking when the unit drops to 10% Strength or a retreat at 10% Organisation marker would help preserve units as would also keeping those retreatable units after they are redirected through another escape route. If they get overtaken or cut off then I'm fine with them being eliminated, although there ought to be a chance based on morale or something of them shattering and reappearing at the Capital or Army HQ etc.
I haven't had major problems with supply yet, but I would like to second what everyone else has said so far on that, in fact I second everything else that has been said except for the building of railways!
