Anonymous cannot see cart in cart page
My guess is you're experiencing a common issue with product permissions due to a relationship you've added from the line item to the referenced product. Open your View's advanced settings fieldset, and in the Query settings menu disable SQL rewriting. This will bypass the normal entity access check to see if a customer has the permission to directly view the related product data, which is fine for this View since we know the products in the cart will always come from line items the customer has created through Add to Cart forms.

See also: https://drupal.org/node/1276450