* The tech system is an unholy unplayable mess that jettisons HOI2's playable streamlining and returns to a HOI1 model where you have to research 12 different elements to build a unit. As a side effect the AI can't research tech at all.
* AI is completely broken - even if you play multiplayer this is an issue unless you have humans playing and micromanaging every nation. If you don't you get the fun spectacle of
the UK building nothing but transports, or the US building 5000 light armor battalions and nothing else.
* The espionage/political system means you have much less control over your own government than anyone else who decides to screw with you
* The theatre AI (which you are required to rely on by the game design) tends to break down with more than one front
* The few events (there are almost none) are broken. For example, there's no reason for the Germans to ever offer the Molotov-Ribbentrop pact to Russia since there's no penalty at all to them for not doing so, and no benefit for doing it. Which is fine since the surrender event for the Russian-German war is also broken. (Literally - it apparently never fires, ever)
* Related to the above, HOI3 essentially throws single-player historical simulation out the window in exchange for a surreal multiplayer-focused sandbox which just happens to take place in a World War 2-era world. This may or may not be a problem for you but most people consider it a step back from HOI2 in that respect.
EU3 was also in a similar "er, WTF" state upon release, was made playable by the 2nd expansion, and with the latest is actually close to what I think the designers were aiming for. But it took a while to get there. HOI3 may have a similar life cycle. But I can't recommend anyone buying it as it stands now.