This question came up in my game group. A player had a completed plot quest that gave him 2 victory points every time he played an intrigue card. Is it possible to play an intrigue card and not resolve the action (either because he can't or doesn't want to) just to earn the victory point bonus? This doesn't seem right to me, but I'm looking for supporting rules.
No, you always have to resolve the card.
The rules say that when you play an intrigue card, you follow its instructions, and none of the intrigue cards have instructions that say "if you feel like it, do X".
Play Intrigue Card: By assigning an Agent to one of the action spaces on Waterdeep Harbor, you play a single Intrigue card from your hand. If you have no Intrigue cards, you cannot assign an Agent to Waterdeep Harbor.
When you play an Intrigue card, you follow its instructions immediately. Its effect takes place just once.
However, as GendoIkari pointed out in the comments, if he actually can't follow some part of the instructions, he would do as much as possible. He'd still be resolving the card, it's just that some instructions are impossible to follow so they don't happen. I don't think there's anything in the rules about this, but if the rules wanted you to ignore the whole card just because you couldn't do part of it, they'd presumably say so.
Side note: your instinct is right; ignoring what cards say in games is pretty much always wrong. If a game has an object (a card, tile, board space, or anything) with instructions printed on it, and you play/use that object, you follow the instructions (insofar as you can). If the game doesn't want you to always follow the instructions, it'll say so in the rules.
I disagree it is my understanding that you have to be able to do all of the intrigue card or not play the card. The reason because,this would allow players to avoid going to somewhere where they could get a skull and lose points. We play very specifically that if it says to do A,B and C you have to do all 3 or you cannot play the card. If you could that would be as similar as skipping your turn which is not allowed either.