You can go into your viewing activity (only available from your account page on the desktop site, I think) and delete the show from there, and then it should remove it from "Continue Watching".

It's not an obvious or straightforward thing to need to do, but seems to work.

That's definitely available in the app as well.

IIRC, "Continue Watching" shows things you haven't finished watching in most-to-least recent order. There isn't any aspect of "recommendation" to it beyond that; you could go find the worst rated, least recommended content on Netflix, play it for a minute, and it'll be first on your "Continue Watching" list.

Have you ever seen something being _recommended_ after you clicked that button?

It's a UX failure. There's no point in recommending something that I've seen and there is almost no way I can know that I don't want to watch something without seeing at least a little bit of it. For all intents and purposes, the "Continue Watching" list is a recommendation of things to watch. If I thumbs down or ask Netflix to stop recommending it, I shouldn't see it prominently displayed anywhere when I open the app.

When I consider these UX fails I often attribute them to the faith in AB testing. It may not be, but it's common for people to complain about X in the Netflix UI and then have either employees or apologists come in and talk about how there have been 100k variants vetted through A/B testing and say the way it works now is the way most people like it. However, this approach tends to fall flat on cross-cutting and more creatively challenging UX concerns. Sometimes you need a Cambrian explosion.

I have a ton of half watched shows that I keep queued for when I'm in the mood, which is usually in the winter. So it works fine for me. It's a reminder of "oh yeah I was watching that before vacation".