My big thing is characters, how well written they are, character dynamics, interactions, and relationships, how complex they are, if they develop and if not, why? How well do they work in the story? All kinds of things. Basically “how much care was put into writing the characters of the anime?”
Also the soundtrack, not that I don’t like anime with not-great or average soundtracks, but when there’s a stellar soundtrack or even just a really great song from a soundtrack, I notice and go bonkers