I don't think Spock having a half brother is a bad thing or that there's anything wrong with it, but I think it's more of a common sense sort of thing. If Spock and Kirk are best friends, chances are that the subject of having any brothers or sisters would come up at some point in a 30 plus year friendship much like me and my two best buds that I've know for 25 plus years. At least that's my take on it.
But he didn't tell Kirk who his father was either. And it's not just "oh, I have a brother who never comes around for a visit." It's "I have a brother who's shamed our people and our family and is an outcast and renegade and we disowned him so he technically isn't part of my family anymore." We know Spock is an intensely private person, and Vulcans have a strict sense of family propriety. Even bringing up Sybok's existence and acknowledging the relationship would've been violating custom. Even on Earth we have instances of families who've disowned members and refused to acknowledge their existence.
Besides, Spock only knew Sybok in his youth. We can safely assume that Sybok was banished before Spock turned seven, since he wasn't in evidence in "Yesteryear." So he would be a distant memory at best, not something Spock would normally give any thought to.
Anyway, the movie offered several explanations for why Spock never brought it up. "I do not often think of the past." "I do not have a brother... I have a half-brother." "I was not prepared to discuss matters of a personal nature." All that is perfectly in character for Spock. If Kirk or McCoy ever asked if he had brothers or sisters, he would've rationalized that technically Sybok wasn't a brother but a half-brother, and felt he could honestly answer "no" and allow them to misinterpret, thus sparing him from having to address a deeply uncomfortable and shameful subject that had no relevance to his adult life.
As far as the Kirk making peace with the Klingons, I think given Kirk's comments about Klingons, "let them die" and so forth is what some people have issues with.
But as I said, that was what was out of continuity, not ST V. Throughout TOS, Kirk was portrayed as someone who was able to look past his anger and soldierly aggression and strive to make peace when the opportunity arose. TUC's introduction of this deep-seated racism against Klingons was a radical retcon, unlike anything we'd ever seen in James Kirk's character for the 26 previous years. It's the exception, so it's bizarre to treat it as the rule.
I just prefer to enjoy the movie instead of worrying about how Nu Kirk has blue eyes, while Kirk prime has greenish brown eyes.
I gather that the word for Shatner's eye color is "hazel."