As for my initial views on the other sons:
Caranthir can be the black-and-white villain, if we need one, either for plot reasons or because we don't have time to give everyone a full story-arch. But we could alternatively have him just be incredibly suspicious by nature, assuming everyone's plotting against his family, so he has to move first. But by his actions, he turns more people into enemies, so now he has to counter-plot against their new plots... until he is defined by treachery and deceit. Remember Eomer's line, that the Rhohirrim do not lie, and therefore are not easily deceived? Caranthir could be the reverse: someone who sees his role as the dissembler and spymaster of his family, and therefore is often deceived into thinking the worst of others, by his own fears and, perhaps, the whispers of the servants of the Enemy...
Yes - if one of them is going to be a straight-up villain, it's Caranthir. He has...fewer...redeeming qualities than the rest. But not none! Just...much harder to spot
He is the proudest, which translates as he is someone who does nothing to hide the fact that he is looking down his nose at you. This is incredibly off-putting, so he has no luck at making friends - he's a complete loner, even within his family (which is more or less tight-knit by necessity). He also has a rather bristly unpleasant personality in general. His brothers tolerate him, of course, but that doesn't mean they like hanging out with him. They give him his space, and try to do damage control to stop him from ruining any chance of an alliance with anyone. Maedhros definitely maintains an 'I'm in charge here, listen to me' stance with him, so there is little friendship there. He likely bounces between hanging out with the twins and hanging out with Celegorm and Curufin, but he's the extra tag-along in either case.
"Maedhros indeed rebuked Caranthir" by Kasiopeia (Catherine Karina Chmiel)
http://kasiopea.art.pl/en/home
He's not a great judge of character. The whole Ulfang-the-Accursed fiasco (the one time someone actually did betray the Fëanoreans!) can be laid firmly at his feet. So, yes, I can see building him up as a suspicious character who sees lies everywhere....and then the one time that is truly the case, he totally misses it. Ulfang likely recognizes that flattery and obeisance will get you everywhere with a proud socially awkward guy like this.
He does, however, have a few unique and positive interactions. He is the first one to befriend the dwarves, though 'friendship' isn't really how I'd characterize that relationship. The dwarves are eminently practical, and willing to overlook his personal failings in order to do business with him. He, in turn, recognizes their skill and usefulness, but doesn't manage to hide the fact that he thinks them short and ugly. [SO not a diplomat, this guy!]
He also is the one who shows up to save Haleth's people after the fact, and is very impressed with her courage and fighting spirit. He never really thought about Men before (well, not in any positive way), but once he saw her, he was all like, 'Hey, do you guys need a home? You can live in my lands....' He wanted to get to know her better. Obviously, that never happened (his invitation wasn't all that gracious and she wasn't interested), but he did make it and I think one could say that Haleth/Caranthir is one of those might-have-been mortal/elf relationships (not even hinted at, but at least from his side, the respect is there, which is so unusual for him as to be noteworthy...and she never married, which fits her character but also leaves open a possibility that there was no one among her people for her). This is *far* from the situation with Aegnor/Andreth (which is mutual, but bad timing) or Túrin/Finduilas (which is mostly one-sided); this is so not-even-there that neither of them are thinking about it. More of an alternate history might-have-been.
The First Meeting of Haleth and Caranthir by Kasiopeia (Catherine Karina Chmiel)
http://tolkiengateway.net/wiki/Category:Images_by_Catherine_Karina_Chmiel
Caranthir character study:
http://www.silmarillionwritersguild.org/reference/characterofthemonth/caranthir.php