1. I realize that Dark Souls and Diablo are entirely different franchises (especially given that DS is currently console only and Diablo is one of the PC's signature games.) That being said, they have more commonalities than differences. They are both cooperative dark fantasy dungeon crawlers centered around challenging boss fights and powerful loot, and they both have the potential for enormous replayability. I think it's useful to compare the two because, unlike D3, Dark Souls has been highly acclaimed for its minimalist but effective storytelling, and a lot of what made DS great could be somehow applied to Diablo.
2. The following contains massive spoilers about Dark Souls, and some minor D3 spoilers. (Of course, if you haven't completed either game yet, you probably won't understand what I'm talking about in the first place.)
Now that that's out of the way, here are eight things that Blizzard could learn from Dark Souls.
1. Maintain some level of ambiguity
This is really the main problem with D3, and most of the following suggestions stem from it in some way.
It wouldn't be fair to say that Diablo 3 shoves the plot down your throat. Diablo 3 drags you into a dark room, ties you to a chair, beats you with the plot until it breaks to pieces, and then slowly forces the jagged remains down your esophagus as Deckard Cain leans over your shoulder and raspily narrates the whole scene in your ear. D3 is a game, not a novel - and even the lengthiest novels have many ambiguous points (so long as their author is the least bit competent.) I'm not saying that there's no room at all for speculation over the plot, but D3's storyline is just not sophisticated enough to hold the player's interest, especially given that Diablo is supposed to be Blizzard's "dark fantasy" franchise. You are good. Demons are bad. You kill the demons. The end. That's pretty much it.
Now, I realize that pretty much any plot can be crudely reduced to a few sentences; it's the individual intricacies of a story that make it worth reading, of course. But D3 severely lacks such intricacy, and rather than trying to expand the storyline by chucking more walls of text at the player, it's imperative that Blizzard reduces the quantity of writing. To use a cliche but valid saying: show, don't tell.
Dark Souls exemplifies the power of showing more and telling less. Apart from the opening cutscene, which is more of a prequel than anything, you're never given a lengthy explanation of the plot; it's not even clear who you are or what you're supposed to be doing. You learn more and more as the game goes on, but most of the information is either gleaned from the one-sentence flavor text on items or the similarly laconic responses of NPCs (who may or may not be telling you the whole truth).
Most importantly, it always feel like you're experiencing the plot. I'm not sure exactly how to express myself here; obviously, you experience the plot in D3 as well, but in Dark Souls it's just more... visceral. I think part of it is that the world itself is the most important aspect of Dark Souls. In Diablo, the environments are mostly just a backdrop for your character's exploits; while the zones are aesthetically diverse, it feels like Blizzard just went down a checklist of the coolest environments and tried to cram in as many as possible. The desert zones, for instance, only differ from the earlier dungeons in that there are tougher monsters and prettier backdrops. I realize that it's a lot harder to inspire a feeling of awe (or fear) when the maps are randomly generated, but it's crucial in any game that the environment tells a story on its own. In Dark Souls, the overwhelming sense of desolation and loneliness that creeps over you as you enter Anor Londo for the first time cannot be evoked through dialogue - and in fact would be destroyed by it. There are no lengthy monologues or cutscenes, but a single glance at the city's austere beauty makes its history painfully clear.
How can a Diablo game achieve the same effect? It's a good question, and not one that I'm entirely sure how to answer (the folks at Blizzard are the ones getting paid, after all). But D3's environments already have a lot of potential, and I think it's just a matter of adjusting the presentation a bit (Act IV, for instance, could be drastically improved just by cutting down the amount of talking and adding some haunting music in the background.)