Belial, The Lord of Lies, has two mouths and four eyes. The two mouths face in opposite directions (left and right of his "head"). Note where the extra eyes are.◊ Belial is "two-faced".
The Blizzcon 2010 demo of Diablo 3 showed that all the doors in Leoric's castle/torture chamber were about 15 feet high and 8 feet wide. Seems like it's just creative exaggeration, but Leoric's Ghost (and skeletal form from Blizzcon 2008) is way bigger than a human. Perhaps the doors were built with him in mind.
You may find it strange that the player character in Diablo 3 is able to identify items and do a Town Portal back to town without using any scrolls, any Mana, or have other characters identify items for you. But consider this...the player characters of the first game were human, so they needed all three methods to accomplish these feats. The players in the second game were either human or depowered Nephalem, so they needed these three methods like before. The player characters in the third game are unambiguously revealed to be fully-powered Nephalem, so they could identify items and use Town Portal as naturally as breathing, and render the three methods unnecessary!
Captain Rumford suddenly vanishes when the Coven attack New Tristram and kill Cain. He doesn't reappear until the finale...as a ghost. Do the math.
You can find his dead body on the way to old Tristram. The PC even says some words when passing, depending on class played.
Act III involves Arreat Crater, a gigantic scar in the earth which is all that is left of Mount Arreat from Diablo 2 after the Worldstone was destroyed. All those barbarians you were helping out in the Lord of Destruction expansion? They most likely met a fiery death. Indeed, Word Of God confirms that Harrogath was destroyed in the explosion, and that Larzuk is definitely dead. However, the fates of the other inhabitants is left ambiguous.
At least one Barbarian survived to become a potential player character (two, if you count both the male and female as canonical) so it's safe to say that at least a few Barbarians are out there. But protecting Arreat was the purpose of their culture, so they've basically been destroyed as a people.
In the larder of Bastion's Keep, you find Ghom's journal, which reveals that not only has he been eating people, but he's also been slaughtering people and feeding them to the unsuspecting denizens of the Keep. The hero and follower don't react to this, but unless they haven't been eating anything at all, they've been eating what everyone else has.
What exactly are the Monk's (and other classes) gods and spirits? When we go to the High Heavens, we only see angels and such. It's possible, one supposes that say Ytar is an angel or non-existent, but both Monk and Witch Doctor both get (or believe they do) get their powers from said beings. One could say that perhaps they're just channeling their nephalem powers (they being the first generation born after the worldstone's destruction), but then where did their predecessors get their power? And it still doesn't explain who beings like Ytar actually are.
How did all the characters at Bastion's keep actually die in act 3-4? (There's no actual battle that occurs, so it makes little sense for the soldiers to get killed unless they went to watch the transition event and got killed as part of that process.)