Now to actually mention a bit about the story.
While I thought it was not bad, it didn't feel very good either. They rushed in a bit too fast for certain plot points, which they explain away with the characters kind of shrugging it all off. It just didn't feel as consistent as D2.
Act 1 was very consistent, it probably had the best use of the narrative and a lot of interesting events, like Cain's death, the reveal of Leah's hidden power, Tyrael's fall from grace and mortality, etc...
Act 2 still moves on a bit strong until we get Adria, and then things just start getting thrown in without explanation. Suddenly she knows about some Black Soulstone that is the key to killing all the Evils, and we go on this long quest to get it by rebuilding some mage, only to find the stone is imbued with the souls of the five dead Evils somehow. Did Adria always have access to his sanctum and the Black Soulstone? How did she collect the essence of the Evils? How did she even get such essence? Didn't the nature of destroying the Soulstones on the Hellforge supposed to be the ultimate death, making it impossible to reform? If part of Diablo was hiding in Leah and that is how he escaped his Soulstones destruction, then how is Mephisto also in there? None of this is touched on or explained.
Act 3 is when it really starts losing it, the story taking almost an entire backseat to the action. Leah is shuffled in another room outside of the town zone. You dungeon crawl down, kill the boss, and move on to the next act with Adria finally revealing her true intentions and merging Leah with the Black Soulstone. (which by this point, was an obvious twist)
Act 4 at that point just became Act 3.5, you don't even get a new town, you just use the same town from Act 3 and the overall time it takes to complete it is half of the others. There is zero closure on things like Imperius, Leah, etc...
Now for my two biggest issues.
Leah - She was probably the main character of the game for me. We saw her in the beginning with the dream, her love for her uncle, we saw her swear to carry on his work, and she was the one that saw the vision of Azmodan invading. She showed no signs of an evil heart, or a wicked soul. Yet when Act 3 came around her character was sidelined and then finally entirely replaced with Diablo. She didn't even get a sentence in before being changed, not even a "Noooo. Mother stop this!". My character and Follower constantly mentioned how they wanted to save her, that her soul might still be there, but they NEVER capitalize on it. The ending is pretty much Diablo is dead, let's toss his ass off our spire so his corpse burns up. Leah? Who the hell is that?
Diablo - This is going to sound really stupid, but Diablo didn't really feel a lot like Diablo, at least with his aesthetics. I know, he is supposed to be all 7 of the Evils merged into a single Prime Evil, I know he is in a woman's body, but something about going from this...
To this.
Just felt a bit jolting, like I almost wish they didn't call him Diablo and just gave the character a new name. The new creature wouldn't have to be the Lord of Terror, but instead the Lord of All Evil. I actually think they did make it so Diablo was the "driver" just because they wanted to make sure, like always, the name of the game fit with the main antagonist.
It also didn't help that in one of the cinematic, Diablo enters heaven with a swagger that makes me think more runway model then Lord of Terror. Did they really have to give him scale plates that make it look like he has breasts?