Sometimes you notice something that doesn't seem right in the TV show that you watch quite a bit. I think that is when you note specific details like, "Why is the sun rising from the west?", sort of thing!
Yesterday's episode of the hugely popular, "Game of Thrones" on HBO had a few posts catch fire about a coffee cup (video below) in plain sight during a critical scene (as this is the final season, every scene is critical, yes?).
It's not new and there are a few sites that are dedicated to sharing little continuity happenings:
This site is pretty good with 15 WORST CONTINUITY MISTAKES IN MOVIES - recent films like, "American Sniper" and one of the "Twilight" character's tattoos shifting around makes for "How Did I miss that" the first time around!
This 2013 article MOVIE MISTAKES: 10 RIDICULOUS MOVIE MISTAKES is a reminder that to enjoy a film, we need to suspend disbelief and go for the ride!