Then there's all the ones with no quest giver than I can't figure out. I think there might be a couple more like that. I only cheat out for quests I've done multiple times and I'm tired of doing, a lot them turned purple that way with less work. But I'm not sure if that is the same as completely doing it. Sometimes I just opt-out by choosing talk after building some random bricks, then she asks if I want her to show me or cancel, I choose cancel, and then it asks me if I'm done, I pick yes and then she'll give me the reward without putting down the special fixtures, some of them will give the reward even if the house symbol isn't checked. I even discovered the fixtures she wanted using the code (discovering anything I used a code for did not add to my discoveries count) and I made sure all the check boxes were checked, and then it was still green.
Also the one in the swamp where you give the crook 4 red and 4 green frogs always stays green, also in the swamp I did the one for the police station build and it always stays green. The quest with the chickens always stays green for me too. It said I still had three quests left to do, but there were only 2 green beacons left on the map.