I'm re[osting this since the link goes to an error page my original question was when various characters "approve" or "disapprove" of an action what if any impact does it have on game play?

I think I can give you at least a partial answer to this. I can not elaborate on how the approval or disapproval actions can change the game direction but I can tell you that if you are trying to romance another companion in the game you want to get their approval in order to be able to romance them. so when you see a heart icon come up during conversations, you simply choose the dialogue for that option. This way you will gain the approval of your object of affection.

Even if you are not romancing, if you choose to many disapproval options with any companion, they can leave your party. I did this accidentally at the start of the game when I was learning the game, and when I went to speak to, I think it was Cassandra, she was angry with me and would barely speak. So, basically you can lose them as a party member if their disapproval gets too high.

Well I've not finished the game yet but I imagine its pretty similar to the previous 2 games, so I'm not sure how useful you'll find this info

What I'll say is that for SOME companions there MAY come a point in a quest where they will leave/refuse to help/turn against you if their approval isn't within a certain range (could be high or low, in the second game you were penalized in a couple of cases if they had middling opinions of you rather then very negative/positive). It likely also affect romances and maybe dialogue choices, but shouldn't impact the core storyline very much, if at all, even if you somehow get everyone to totally hate you :P

EDIT: I'm further into the game now and it does seem that at least some of the characters need a high approval rating before some of their personal quests trigger. These are relatively short side quests which don't matter much gameplay wise unless you want to romance that character (though they are certainly well worth doing imo)