I know mechanical pencils are prohibited, but what about mechanical erasers? I prefer them over block erasers because they're more precise.
Are you talking about one where you click it to make more eraser come out of the end? Other than that I'm not sure what you could mean by 'mechanical eraser'. The language of the LSAC rules just says that erasers are allowed but does not define what types. I would guess that since they banned mechanical pencils (for whatever reason, why is still a mystery to me!), and that since a 'mechanical' stick eraser is similar to and resembles a mechanical pencil, that it would qualify as a banned item.
Play it safe and get used to using a block eraser. Hello Kitty ones are kinda cool still!