"Where television is fantastic, and is way ahead of film, is it doesn’t feel the need to polarize women so much. Male writers often wanna make a woman either the angel or the whore. Make her the witch or put her on a pedestal. They’re not mutually exclusive. You don’t have to be practical, politically savvy, and not be a good person. You can be a good human being and be shrewd. They’re not two separate things. We are as complex and contradictory as the men." - Natalie Dormer
Actually I’ve seen people mention it since the first episode.
It’s Capaldi’s wedding ring. He never takes it off, even when acting.
To add to the story, he refuses to take it off because when his acting career was struggling, his wife never gave up on him. When he landed his first major gig, he decided to not take it off, to represent he was there because of his wife’s support.