What would castle characters think if they watched castle fanfiction?
Well, it really depends on the specific characters. For example, Castle himself might be flattered by some of the fanfiction that portrays him as an even greater detective or a more charming writer. Beckett, on the other hand, might be a bit more reserved in her reaction. She could be critical of any fanfiction that strays too far from the facts or that misrepresents her in a way she doesn't like. And the other minor characters like Ryan and Esposito might just have a good laugh about it all, enjoying seeing themselves in different fictional scenarios.
The castle characters would probably have a very mixed reaction if they watched castle fanfiction. Fanfiction often takes the essence of the original characters and stories and twists them in new and unexpected ways. Castle, being a writer, might initially be intrigued by the creativity of the fanfiction writers. He could see it as a form of flattery that people are so inspired by his world that they create their own stories. Beckett, who is more practical and grounded, might be more skeptical. She might worry that some of the fanfiction could mislead fans about the real nature of their investigations or relationships. As for the supporting characters, they might be entertained by seeing themselves in different lights, but also might be a bit uncomfortable with some of the more out - there interpretations.