If you want to tweak the permissions, you can use a plugin like Members and add the book-review capabilities to the roles you want to add. By default, the only users who cannot post reviews are subscribers and contributors — everyone else can at least post their own reviews. Librarians, Editors and Administrators can also edit other people’s reviews.
There’s no built-in capability to tweak these permissions but there are other plugins that can be used for that purpose.