Hearts of Iron III

Whenever I purchase a newly released game from Paradox Interactive (PI), I always think of that excerpt from Henry V: "Once more [into] the breach, dear friends ...". It is a good bet that there will be two big scoops of bugs, underneath which there will be complex mechanics and hours of fun. HOI3 is, in a nutshell, pretty much that.
 
So, let's start from the top.
 

Size

 First and foremost, this game is huge. And not in that "it has resources, diplomacy, intelligence, etc" huge - but rather in that "holy god, the map is sub-divided into 10,000+ provinces" huge - although, approx. 14,000 is perhaps more accurate. 
 
At the risk of being long winded, it's useful to consider why this is a great thing. When considering an arbitrarily-sized military operation, the tactics which can be employed are relative to the degree of freedom of movement the aforementioned military has. For example, if the entire theatre comprising an operation consists of 10 large provinces, it is a) easier for your opponent to "stack the line" with hardened units, and b) harder for you to exploit specific tactics like encirclement, supply cutoff's, etc.
 
By enlarging the number of provinces and further subdividing the world into smaller provinces, tactics like those previously mentioned become more pertinent, and furthermore they are exploitable against smaller sections of the enemy, as opposed to their entire force.
 
Whether that explanation does the system justice or not is questionable, but the bottom line is that it works quite well and adds a great layer of tactical consideration to the game.
 

Supply/Logistics

Further increasing complexity in military operations is the addition of a supply system. It is a great idea, and even occasionally works really well. The rest of the time, however, it has the potential to be an unmitigated nightmare of micromanagement and thrashing.
 
The basic premise is simple: all units consume a specific amount of supplies (technology/etc influences this number), your capital produces a specific amount of supplies, and the job of the supply system is to route supplies from your capital to your units.
 
Bear in mind that this system is, more or less, controlled by the AI. Now, you can help it out by building infrastructure "highways" through vast swaths of your territory and researching technologies, but these are "hints" at best. This wouldn't be a problem if the AI understood exactly what you wanted, but it doesn't and, for that matter, can't. So, the position of the AI is simple: I will supply how I want to, and you can deal with it however you want.
 
This is a major bummer because I find that when I'm cooking up a battle plan, I'm always asking myself if the supply system will cooperate with me. Notice that I'm not saying the supply system doesn't work, but rather that it doesn't work how I want it to - and not in a personal way, but rather in a context-sensitive way.
 
Over the course of a single war in this game, a plethora of strategies will be employed to win on various fronts - and as such, supply needs vary. If there was a way for the player to specifically route supplies in a specific direction (e.g.: "desupply" other units in favor of others) or stockpile them in a specific spot (say, for example, stockpile supplies from side A, then suddenly route all other supplies to side B while side A can rely on its stockpile; thus, attack from both sides whole only supplying one) then the AI would be more then adequate. Alas, this is not the case, and so you will be building a lot of infrastructure, [upgrading] naval ports, air supplying, etc.
 
So, again, the supply system is not broken. You just have to play within its rules, and if you do, everything will be fine. If you don't, things can get ... ugly.
 

Officers

Officers are another nice touch to the military in this game. The effectiveness at which your military units can operate is controlled by the percentage of officers you have for your current force, with maximum benefits at a 2:1 (200%) ratio.
 
It is fairly abstract, in the sense that officers are created by a slider, but it works well.

Command Structure

The command structure is pretty nicely setup. It is a hierarchy of "group commands", each successively smaller then the previous.
 
 The actual hierarchy is (Theatre->Army Group->Army->Corps->Division->Brigade), and it allows a good amount of granularity in your commands, depending on how "hands off" you want to be - anything above a Division can be set to AI control. Also, depending on who you have leading them and their skill level, the HQ's provide different benefits to their units. 
 
Another good feature is the ability to set AI HQ's a variety of objectives (multiple provinces), and a specific stance which dictates how they will respond to those objectives (defensive stance, attacking stance, blitzkrieg, etc).
 
All in all, this system works quite well.
 

Technology

You research technologies, they confer the ability to build new units, upgrade existing units, upgrade provinces, etc.
It does its job, with few complaints.
 
All the technology names/descriptions are another nice touch worth mentioning.
 
The rate at which (and the number of projects you can research) is controlled by a slider.
 

Diplomacy

You can take a variety of actions (trade embargo's, influence a country to a specific faction, declare war, etc), which is nice.
 
When it comes to war, two things (your ability to win the war withstanding) matter: neutrality and threat.
 
Neutrality is how neutral a country is, relative to the world going on around them. War can only be declared when a countries neutrality is lower than an opposing countries threat level.
 
Threat, as it sounds, is how big of a threat a country represents to the world around them. Calculated on a per country basis (Germany has a different threat to Poland than to Japan), this is raised by fielding a massive military, "mobilizing" reserve units, declaring war, etc.
 
Another feature is when you conquer a country, you have the option to "puppet" them, which basically makes them "tow the line" with whatever you do. There are also some occupation policies, which can increase/reduce the amount  of bonuses you receive (production bonuses, etc).
 
Various diplomatic actions require Diplomatic Influence, which is a pool of influence points which you generate based on a slider.
 
However, there are some problems.
 
There are some complaints about how various fixes to the game reduce the amount of trade offered by the AI, other complaints about how sometimes the diplomacy gets tangled up in itself (a country in a particular faction can be at war with other members of the faction, etc), and some "puppet" problems (supplies won't move through them).

Intelligence

A good system with the ability to prioritize specific countries for your spies to infiltrate, with a great variety of missions for them to fulfill. You can also assign your domestic spies a specific mission.

There are some annoying, "off the beaten path" bugs, though. For example, sometimes a nation will be conquered/annexed, the game won't remove their spies, and save for editing a file, they become immortal and quite a nuisance.
 
A small complaint I have is if you could assign a number (or percentage) of spies in a country to a separate mission - or, more simply, multiple missions per country. This would be better then toggling the mission every few days, month, or what not. 
 
You control the rate at which you generate spies with a slider.
 

Sliders, and their AI

There are two slider setups in HOI3. One of them works ok, the other might annoy you quite a bit.
 
The first one to talk about is the Leadership slider, which determines the research speed/amount, and the generation rates of diplomatic influence, spies, and officers. This slider works pretty well - four sliders, which can be locked and unlocked.
 
There is also the Industrial Capacity (IC) slider, which distributes points to Upgrades, Reinforcements, Supplies, Production, and Consumer Goods. This one also works fine, as long as you open it almost every day and "relock" the various sliders.
 
There are (as of v1.2) AI options to set different priorities to the various sliders, and they adjust better then they used to. There are also several community modfixes out there. It is possible to get them working right, but if you like to micromanage your sliders, you will do a lot of it if you leave it on manual.
 

World War II

The game, in certain glaring spots, is not historical. There is no Pearl Harbor, it is possible for the USA to drift into the Axis, Japan is occasionally brain dead and useless, and several other annoying things.
 
On the other hand, when you are able to drag the USA into the Axis as Germany, and give the USSR a run for its money, there is a certain enjoyment in that - one which a purely historical game couldn't do.
 
So, if you want a pedantically historical game, and the absence of Pearl Harbor annoys you, this may not be what you want.
 

Weather

An absent feature. Then again, an absent feature doesn't penalize the game - the weather in HOI3, on the other hand, does.
 
Pretty much every ocean province in the game has rain - in fact, it seems like there is a global typhoon going on. The land weather is a little better, but large parts of geographic areas are either gripped by perpetual rain or have similar weather anomalies.
 
An annoying consequence of this is the almost complete ineffectiveness of aircraft carriers. On top of that, it seems the friendly fire rate goes up when there is bad weather, which results in some pretty amusing (and not-so-amusing) friendly-on-friendly action.
 
There are some modfixes out there that can help, but they range from disabling all weather to reducing the problem but with side-effects.
 

Closing Remarks

HOI3 had, and has, some particularly nasty bugs - extreme lag/slowdown in later years of game (1941+; helped by v1.2), map anomalies (border problems, several important cities not being located where they should), crash-to-desktop bugs, savegame corruptions, weather severely hampers gameplay, major countries' AI (United Kingdom has a particular affinity for transport ships, Japan likes to count sheep), and several others.
 
This can, and has, ruined several games for me. However, when it works well enough, the game is very enjoyable and there is a lot of depth there - having an AI front distract an enemy and then micromanaging the real invasion force is strangely rewarding on some kind of deep spiritual level. And handling supply problems is, dare I say it, sometimes fun and refreshing.
 
HOI3 is a good game, some of the time. The rest of the time it might work, but you'll be fighting it.
 
It's not a bad game, but it isn't what it should be. The upside here is that, PI's record being what it is, the game will probably only get better over time - consider it a fine wine that hasn't peaked yet.