Sarek. Are you kidding? He's almost more of an important legacy character than some of the "B"-level TOS 1701 crew. Besides that, in TVH, it made sense for Sarek to travel to Earth to defend the people who made it possible for his son to be restored to life. He was acting like a very understanding, grateful parent.
Also, being the Vulcan ambassador to Earth, his presence makes perfect sense. If they used some unknown ambassador, fans to this day would be saying they should have brought back Sarek.
Yes. Carol was the lead scientist involved in the development of Genesis. It was her project. For her to completely vanish and have no further involvement once the Genesis planet was created makes absolutely no sense.
She should have been mentioned, even if they didn't want to use Bibi Besch. David being on site and Carol doing lab work. And yeah, I know they didn't want to load up the funny movie with anything heavy, but Carol and Kirk should have had an on screen conversation in The Voyage Home.
With just a few lines of dialog, without delaying all of the yukity yuks, they could have put some actual buttons on some of it. Without even hiring Bibi Besch - just mention her.
"Jim, how did Carol take the news...?
"How would you take it, Bones?"
"Maybe she'll..."
"Not for a long time."
Boom, Carol situation resolved.
Saavik would have been better served by putting her in the courtroom scenes. Either way, she was insultingly ushered off the franchise before the fun started. She finally - after three months - thinks Kirk "should know" that David "died most bravely." Where's she been for all this time? Did she immediately leave for Earth to report? She wasn't in trouble. Did Kirk refuse to talk about it? No mention about that from him (in fact David is off his mind until TUC).
It's like these were characters they regretted introducing movies earlier because they wanted to get back to the original TOS formula. Which, great, it's an awesome formula, but I was enjoying the evolution.