Updated tutorial code for Om 0.1.6. See more at http://www.lexicallyscoped.com/2013/12/25/slice-of-reactjs-and-cljs.html

slice-of-react.clj

;; Updated tutorial code for Om 0.1.6, 2014-01-16
;; http://www.lexicallyscoped.com/2013/12/25/slice-of-reactjs-and-cljs.html
;; See comments below for details on the changes.

(def app-state
  (atom {:comments [{:author "Pete Hunt" :text "This is a comment."}
                    {:author "Jordan Walke" :text "This is *another* coment"}]}))

(defn comment [{:keys [author text]} owner]
  (om/component
   (dom/div #js {:className "comment"}
            (dom/h2 nil author)
            (dom/span nil text))))

(defn change-author [cs new-author]
  ;; The cursors internal path is used, no explicit path needed
  (om/update! cs (fn [comments]
                  (mapv #(assoc % :author new-author) comments))))

(defn comment-list [cs owner]
  (om/component
   (dom/div nil
            (dom/div #js {:className "commentList"}
                     ;; Helper function build-all builds a vector of components
                     (om/build-all comment cs))
            (dom/button #js {:onClick #(change-author cs "Fredrik")}
                        "Change authors"))))

(defn comment-box [state owner]
  (om/component
   (dom/div #js {:className "commentBox"}
            (dom/h1 nil "Comment")
            ;; Cursors support lookups to yield new cursors, so
            ;; they can be used directly to pass sub-state,
            ;; maintaining paths internally
            (om/build comment-list (:comments state)))))

(om/root
 app-state
 comment-box
 (.getElementById js/document "content"))

I think comment-box needs to appear before app-state in your arguments list starting at line 39.