The Hearts of Iron series is never for the faint hearted. HOI 3 has vast potentials but currently feels unfinished.
While in HOI 1 there are about 1000 provinces in the world, in HOI 2 there are 3000. Now in HOI 3, they tripled the number again and with 12000+ places the game become a serious challenge to one's gaming rigs. On my Core i7 + 6G system, 1 real life minue ~= 3 days during peace time and can lag to < 1 day in wars. There are already user contributed patches to make time tick faster, but I doubt most people can enjoy the game unless an official patch boosts the speed 3-4 times.
Nevertheless, the huge amount of provinces is really contributing to the strategy and depth of game. You can now encircle and surround your foes with much more choices. This would be a very exciting experience only if the AI work properly. While the AI do work fine most of times, it can occasionally also do strange things like ignoring its allies or not defending its critical locations. Theres still much work to do for Paradox team.
Don't get me wrong, I totally love this game, I only want it to be better. The interface has been improved a lot from HOI 2 and it is quite pleasant looking (Altho HOI is never a game about graphics). The theme music is awesome, and there are some very cool tracks too. The learning curve is very steep, 80% of people just gave up when they got totally dumfunded by the sheer amount of digits and icons. But I assure you this game is very rewarding after you mastered it, especially if you have a taste of historic strategy war games.