1. Improvements to the overall atmosphere of the Diablo universe. Darkness, blood, death and fear. Of course add some more vivid areas for contrast.
2. Cut down on the references to people / celebrities / real life stuff when it comes to items for example. And all the "silly stuff" that just makes immersion into the game a tad more difficult. (Hamburgers, rainbow swords, thunderfury?!) There's plenty of Diablo lore to absorb influence from.
3. Get rid of the current item set design where item sets are pretty much bound to a certain skill. You could add the current item set powers for example to a skill tree. Then add some truly legendary powers to the sets / epix.
4. Make the NPC's serious..."my stomach feels strange..."
5. Go easy on the damage numbers. I Don't want to brag to my friends that i crit a monster for 1,2 trillion. It doesn't feel authentic.
6. Bosses should be hard!
7. Add a new very rare item tier. Finding a legendary item does not feel very legendary at any phase of D3. Make the character feel powerful wearing legendaries. Then make the character feel like a god when you find some of these very rare items. The item hunt, which is pretty much the essence of Diablo, is too dumbed down at the moment.
8. Make armor sets look simple but cool.