The world of anime is filled with all kinds of crazy, fantastical and insane situations. It just comes with the territory, and it's part of why we love anime so much. The ideas that anime puts forth are sort-of no holds barred. The animators and creators go wherever they want to when telling a story, and we're just along for the ride. You better be ready to go to some places you've never been before!
Sometimes those story twists and turns take us into some very unique and...tough to explain situations. An anime could be about serious topics like love and betrayal, but some points in the series could be nothing more than fan service. You and I know that those points in a series don't speak for the overall goals and path of the story, but those that don't watch anime don't know that.
For example, let's take a scene in Fooly Cooly. This series is full to the brim with all kinds of insane imagery. That's the the taboo kind of content that may make you blush when someone walks in on you watching. One scene in the series shows the main female lead Haruko laying down right on top of the male lead Naota, who just happens to be a young boy. Making things even more 'interesting' is the fact that Haruko is wearing nothing but a skimpy nightgown that doesn't really offer much coverage below the waist. If you're involved with the series up to that point, you know exactly what's going on and why it makes sense for the story. For the average joe, walking in on that would look like an extremely inappropriate scene.
What anime you have seen that might get you in trouble if caught at the wrong time? Every anime takes a few tangents along the way, and some of them might be quite taboo for someone that just stumbles onto a viewing. What we take for granted could turn someone else away in an instant!