Okay, here are some additional ideas I think could make some items truly unique:
1. A weapon which requires extreme concentration to use - you don't remember all of the six skills available to you. When equipped - a skill slot is disabled.
2. A huge sword which requires a lot of space around you in order to inflict maximum damage: Damage inversely proportional to your distance to nearest wall.
3. A magical amulet which draws powers from people nearby: its properties amplify as you stand closer to other players/followers.
4. Weapon that works best/worst during the night / in rain / in buildings / when facing south / etc.
You know, it could have a mini backstory like "the gods of the north will enhance the damage inflicted by this weapon as long as you don't turn your back on them." This could actually alter the playing style
5. Intimidating item which speeds up the dialogues with NPCs.
Please share your thoughts about these Any any other ideas you have!
All these ideas create complications that isn't the style of Diablo.
Stronger during day/night? What if you're indoors? Would this make you stop playing for half the time just to wait for your maximum strength to come back?
In buildings? Does this mean you'll be switching weapons once you enter/exit a building?
Always facing south when you fight? That makes for awkward positioning, and positioning is a big part of Diablo, but only to pull off your skills in the most effective manner. For example, you have the skill molten arrow (shoots a line of fire that continues through enemies) on your demon hunter and the enemies are clustered in a crude line facing east/west. This situation calls for more efficient kills without having to obey the rules of some awkward item stat like shoot south for +20% damage bonuses.
I have issues with all your points, but I'll leave it at this.