Christopher, please define continuity and answer this question, does this show have continuity? Make it short and stupid for this layperson. When I see wall of text, my eyes roll and I am like, "TL; DR".
I don't think anyone needs to define continuity. The point is about realizing there are priorities beyond simpleminded dogma. Important
continuity in a work of fiction is in things like characterization and plot -- making sure that characters' behavior and motivations are consistent or that the important events of the narrative are remembered. Things like the design of a piece of equipment or the details of a throwaway historical reference or the appearance of a character who's been recast... those aren't essential to the story. They're matters of interpretation.
That's the word you need to have defined: interpretation
. Every storyteller is interpreting a set of ideas for the audience, making choices about how to present them and what details to employ or emphasize. And every storyteller's interpretation of the same idea is going to be different. Even the same storyteller's interpretation will change over time as the storyteller matures. Because fiction is a personal expression, and that makes it mutable. Two different actors playing the same character will play it differently. Two different comic-book artists drawing the same superhero will draw her differently. Two different historians describing the same event in history will describe it differently. But neither of them is "wrong." They just have different interpretations, because they're individuals.