Ok, I haven' t read any of the suggestions above but here are mine:
1- New buildings, a lot of new buildings, like:
1a- Research center/university: like the rocket site and the reactor it should be allowed just in one province with a max quantity set by a technology (ie. Max_research_center= 3). This building will increase the research speed, increase the ability to gain a blueprint, add an extra slot to research (ie. if you can use just three tech teams, with this building you could use four)
1b- Intelligence agency: like above, just in one province with max size. This building would increase the ability of performing intelligence actions, send spies, coup nations and so on.
1c- land units training ground: in HOI2 you create units and then they pop up wherever you want in your territory. Well, not wherever you want actually. If you play with Great Britain you will be able to deploy your units only on the island. With the "land unit training ground" in one province you will product and deploy the unit in that province (ie. you have a "land unit training ground" in Bombay; you will create one infantry unit using this facility and, when the production is over, the unit will deploy in Bombay). The bigger the facility, the more units you will be able to create, of course if you have the necessary IC, this do not eliminate the need for IC.
1d- Shipyard: like above but for ships. It would need at least a naval base though.
1e- Airplane production: like above but for planes. It would need at least an airfield.
1f- Army HQ: doctrines will be researched more quickly, leaders will be more effective, morale will be higher, organization will be higher. This is a one-province-only building, like the reactor.
1g- Of course, if someone bombs these facilities bad things will happen, trust me, BAAAD things: research will slow down, spies will die, production will slow down and morale/organization will decrease.
2- You play as Italy and somehow you want to see Malta as a free nation. You should be able to press for the release of Malta with a diplomatic action (and/or with an intelligence action) so that Malta could be released by the United Kingdom. With intelligence you should be able to arm the partisans giving them better training, units and so on, making it easier to fight the oppressor. Of course this is not just about Malta. This is about every non-free nation, so you could do the same for Texas, Armenia or even the Netherlands after the german invasion. In HOI2 you can form partisans, my idea is to be able to improve the partisan activity and strenght.
3- There' s just one Berlin. But what if the allied and the soviets win the war and decide to split Germany and Berlin (like the did). If this happen Berlin (like Trieste, Jerusalem or Wien) should be split in two provinces.
4- Airplanes brigades: like napalm for a CAS should make it more effective agains a city, a jungle or a forest, cluster bombs would be perfect against large enemy armys, fighters with a radar would be more effective.
5- Tech teams gain experience: they should be able to gain some experience after developing a technology.
6- Ability to increase nationalism with internal propaganda, so increasing the troops' morale.
7- International and national waters: if you are not at war with another nation or you don' t have the right of passage you should not be able to enter its territory, not even on national water.
8- Attack, support attack, siege! Siege would slow the enemy supplies or, if performed by enough units, totally stop the enemy supplies in a province. Best performed in an urban area. This can be done by naval units to a province with a naval base aswell. This action would cause few casualties un both sides (but the units performing a siege will see their organization decrease)
9- A third nation should be able to try to make two nations in war with eachother sign a peace treaty.
10- If a unit is destroyed by the enemy or by the lack of supplies, its leader should no longer be available.
11- Land and costal forts should have their own defense. With other troops in the same province the defense would increase. It' s not like you create a fort without troops and cannons. If a enemy unit attacks a province with a fort and without units it should still engage combat.
12- Events such as the Nurberg Trial, the partition of Germany, the Surrender of Japan (or any other nation in WWII) after the use of atomic bombs, the Marshall Plan, war in french Indochina, and many events with quotations from Churchill, Roosevelt, De Gaulle, Hitler, Tojo, Stalin or Mussolini (or else) to increase the troops' morale or decrease dissent.
13- When improving the infrastructure in a province with infr higher then 80% it should decrease of 10% while building. When the production is over you will get that 10% back plus the 10% you just produced. Why? Well, if you build in a site with few infrastructure you don' t touch the ones already existing but if you build in a site with planty infrastructure you are just going to improve the ones already existing, blocking them partially to accomplish the task.
14- Buy maps. With intelligence you should be able to buy the map of a specific enemy region, showing you how many troops there are and what kind of troop there are. This should work for, let' s say, 12 hours max. Of course, like every intelligence action this won' t always be succesful, you' d need the right number of spies, the right decription technology and so on.