*Biggest, almost universal complaint is related to the itemization. Unique drops are very infrequent and are generally outclassed by Magics/Rares. Their stats aren't really that impressive in the end game.
*Infernal mode is too difficult and doesn't seem to be properly balanced among the classes.
*DRM issues. Lag, server drop outs, constant maintenance barring you from play, AH has weird delays/issues. Que "I am getting lag in my single player game" complaint.
*Weird hit boxes which cause enemies to attack you even when you are out of their visual attack box range. Makes dodging very ineffective in the game.
*Weird design choices. Global EXP after completing quests is broken because it allows you to boost lower level characters, way points pretty much useless, public games system is really off etc.
*AH breaks a lot of general concepts/mechanics in Diablo. Crafting is garbage because of it and there is less incentive to go for Magic find builds than Gold find builds. Gem system is also borked thanks to AH (why make your own when you can buy them for cheap). Less incentive to trade and farm in general.
*Story has crap writing, dialogue overall is pretty bad too with few exceptions.
*Graphics are on the lower end and even then a lot of high end PC don't run it properly. It doesn't seem to be properly optimized.
Probably a few more I am missing. But the game does a lot of good too.
I would add that map generation is restricted compared to Diablo II. Part of a given map is randomly generated, but there's also plenty of permanent section as well so you do get the feeling of redoing mostly the same one over and over.