I wanted to make a topic along these lines but this already exists so I'll just post here.
I think Dwarves should not only be more social, they should be in conflict more often. As of now, the only times dwarves fight is either tantruming or getting into drunken bar brawls. I think this should be expanded upon. Two dwarves that already hold a grudge against each other may end up in a physical altercation similar to a bar brawl. It shouldn't be to the death--just bruising, minor cuts, MAYBE a broken bone if something goes wrong. Other dwarves nearby may either watch, avert their eyes and go away, try to pull the fight apart, run away and call the fortress guard if it exists, or even join in if they support one of the fighters. They can feel a variety of emotions from: they might find the fight thrilling, they might be scared because they don't like violence, they might feel that one side is justified, etc. If nearby stuff, Dwarves might grab these things and use them as misc. objects--for instance, beating their opponent with a mug.
These fights would not be crimes unless someone got seriously hurt--at best, the fortress guard will come in and break it up and send everyone way, and serial brawlers may suffer more severe punishments (I could go into a tangent about how the guard should do more than just beat people to death and/or jail them but that's for another time; I will say that being able to dodge and evade the fortress guard before they arrive would be neat though). Not only does this add flavor, it also means hospitals are useful for things other than just wars and tantrums. Also, dwarves wielding weapons such as soldiers or hunters should put them away, cast them aside, or at the very least NOT use them (with using weapons being a straight-up crime)...
...unless they are under a lot of stress. A dwarf who's severely stressed might snap into a full blown tantrum during a fight, resulting in them fighting lethally, which causes everyone to freak the fuck out. This would be a flat-out crime. Building off of this, we can have cool things like gangs of dwarves that get into full blown gang wars against each other inside the fort. Fun!
For something a BIT less violent, Dwarves should be able to communicate with others when doing jobs and also when a few tiles away. My three metalsmiths should chat with each other while forging gold crafts, perhaps becoming friends, or enemies, or rivals. A rival nearby could motivate a dwarf to work faster and/or better (or maybe worse if they're working TOO fast).
I think it would also be cool if dwarves had opinions on stuff besides preferences. For instance a metalsmith could look down on carpentry and thus mock or tease the local woodworkers if they're particularly vindictive or cruel, nursing grudges that can go on to become full blown fights if they keep pushing it. Likewise, they'll have a very minor negative thought about seeing too many wooden objects around, especially those that could be made with metal instead. The general viewpoint of a civ on various jobs could be defined in ethics: Dwarves for instance, would generally find metalworking, stonecrafting, and masonry to be more respectable than woodworking or bone carving, but of course individual dwarves could still like those, and dwarves with those professions would be very strongly biased towards them. Fostering a relationship with a dwarf whose profession you don't care for could raise your opinion of the job/dwarf ("Wood may be for the elves, but Urist McWoodworker? He's as good of a carpenter as I'll ever see"), as could said dwarf making a masterpiece artifact or somehow impressing you in some way. BUT, a grudge against a dwarf whose profession you already dislike would only strengthen your dislike ("Of course that fuckin' bellend Urist is a woodworker--should go live with those prancing Elves, by Armok")
Put simply: Dwarves' socializing should do more stuff. As of now, it doesn't really do a whole lot--a dwarf socializing does very little interesting from a gameplay perspective. Dwarves fighting with each other, intentionally avoiding ones who annoy them, hanging out with friends, competing with rivals, and making their opinions on stuff known and causing conflicts and friendship via those opinions, would all be amazing features, I feel.