Overall I'd like the Paradox to have mechanics for more significant things that happened historically, even if they happened only couple of times. That would significantly increase "potentiality" that would exist as a result of interaction between economic, military, diplomatic, research and intelligence factors. I think that would result in the game becoming less a school-level interactive history textbook-play and more of an academic level agent-based type system.
1) Ultimatums? "Unless you give us... we'll go to war". From 20th century history we know this includes bases, friendly government, puppet status, annexation, territory, biased trade treaties, alliances, stopping mobilization.
2) Economic buildup towards autocracy in strategic sectors?
3) Overall huge amount of resources invested in "potential" projects (including "insane" ones like ice aircraft carriers, batbombs, biological weapons, super-planes, etc) that never got anywhere close to killing even 1 enemy. Because at the time it was unknown what will and what will not result into real application. Building our bias into game mechanics forbids and narrows down potentiality paths.
4) Causes and effects systems from internal to external workings of a country. Building up your autocracy? Building divisions? Researching military tech? Adopting ever-more militaristic laws? AND MOVING ALL YOUR ARMIES TO BORDERS?? (you're insane to do that in real life unless you want to go to war the next week). Your threat should not just go up, it should skyrocket. If Germany historically did all those things as it does in game then it should be at war by 1937.
5) Fifth columns. What Germany did with German communities in Czechoslovakia, Poland, Austria, Lithuania, Latvia, Estonia was a huge success for its propaganda and intelligence networks.
6) Something akin to "fifth columns" aka collaboration. The previous point pales in comparison to how successfully Germany and Japan managed to actually recruit and maintain allegiance of Russians and Chinese who in hundreds and maybe millions not just agreed to collaborate passively, but actually fought alongside the Germans and Japanese.
You can also look at this from Allied perspective - it was a success of Allied propaganda to get Italians on their side by the end of the war. It didn't just "happen". Allies actually spent resources to get those results. So why not let player choose *where* those resources should be spent? Maybe its more important to get Sweden into Allies instead of getting widespread collaboration from occupied Italians?
7) All other types of Intelligence warfare. Sorry to say but Intelligence has been a very limited success in HOI2, in DH and in Hoi3. Its just not fun. Its tedious. Its boring. It feels shallow. How much effort did Britain historically put into intelligence warfare? How many resources and effort did Soviet Union put into its intelligence networks that were probably the best in the world - capable of stealing nuclear secrets not once, but on continuous basis, multiple times?
8) National Unity concept is a good step forwards, but its not really enough.
9) International conferences with major consequences for Europe? Happened in 19th century. Could have happened and avoided WW1. Happened in Munich, 1938 but with ridiculous results. Might have happened in 1939, for example concerning Polish corridor.
10) Personalities of ministers of your government influencing your government time to time based on their own priorities and type of government you have. Player shouldn't have "full control". Does player have "full control" in for example CK2? No, it has control to influence and lead towards. Not sure if ministers are still in-game, I think they're out..
11) Foreign arms sales. A significant part of military diplomacy should be the global market of military goods. Not just some rares and metals, but real goods. Because majority of countries were not producers of their own military equipment (except light equipment). Also, economic model in Hoi series is quite unrealistic. There were plenty of states that relied on export of consumer goods to get international currency to spend it on military goods. Here, you have to have local military strategic resources to be able to produce the consumer goods.
12) Please leave the political laws in-game, but do expand number of them, less-streamline them. 15 type of laws would allow to individualize and represent all types of countries that existed, especially if requisites would be closely linked with other parameters of the state.
13) Custom states. The possibility in EUIV to create unique states should be here as well. After all, Lokot autonomy was one such puppet state. Reichkommissariats would be exactly the same - artificial states that are also supposed to be colonial states, like French Algeria. General Government - exactly the same, an artificial state. Why pre-set them and not allow any others when instead they should just be in a list of possible state names for artificial states created by specific countries. Soviet Union had no problem creating artificial state of "Finnish Democratic Republic". It should have no problem creating "British People's Republic" as well. Or "People's republic of South Africa".
14) Movement of industries as a mechanics available for all countries.
15) Movement of manpower as a mechanics for all. Did Finland move its "manpower" from lost provinces? Definitely. Would it have moved its "industry" as well if more time would be available? Absolutely, though it should depend on the peace treaty terms. Should Romania have chance of moving its manpower and industry from Moldavia? Yes. Give those tools to players, please.
16) Core, claims and development of cores. Should Soviet Union have any difficulty of coring provinces of Gobi Desert? Having an algorithm for coring that has modifiers of manpower amount, industry amount, terrain and distance from nearest existing core and amount of any other infrastructure objects in the province - would be easy. For example, should Gdansk province have German core in 1944? Definitely. Should Soviet Union have cores in rural provinces of Western Belarus in 1948? Yes, definitely. But not in cities that fast. Also, the Italians should have a realistic chance of coring at least parts of Libyan coast, as they did historically. What if they stayed out of war, prepared for longer and entered the war in 1944? By that time a couple of Libyan cities should be cored.
17) Dynamic mechanism for damaging and permanently reducing industry and manpower. Why should population of London be ignorant and not evacuate if German invaders in Kent have been trying to cross river Themes for the third year straight? Why should Stalingrad still have any sight of manpower when 95% of its buildings no longer exist in 1943? I don't think this is difficult. Does Crusader Kings 2 have dynamic spread of technology? Yes it does. Can population and industry obey to similar rules (influenced by state laws, for example totalitarian state forbidding evacuation instead preferring full loss of manpower in fear of dissent from panic) in HoiIV?
18) Include potentiality for post-WW2, cold-war processes, like proxy warfare. Because what was Spanish Civil war if not at least partly a war hijacked by global powers to battle out their differences, enlarge their sphere of influence, test and improve their weapons? Greek civil war was one such as well and it definitely was within game timeframe.
19) If you have some type of global arms market then linking it with intelligence warfare tools for supporting proxy warfare should become very realistic and fun. Why shouldn't USA player have chance of profiting from war in USA by selling some strategic goods to multiple parties via neutral countries that are also trying to profit from such transactions? And plus, why should a fully democratic country have full control over some private trade deals of metal ore..
20) Dynamic system that leads to more then 3 major alliance. Japan should have chance of having their own major alliance especially if they successfully buildup their Greater Prosperity Sphere and have control over majority of China, South-East Asia and India. They should by that time be in no need for patronage from some German-led alliance. Also, it would simplify the life of modders greatly.