Cart Should Update on "Review & Checkout"
From various reports, it seems users can easily overlook the "Update Cart" button or it is not clear that this button must be clicked in order to save changes to the cart before clicking "Review Order & Checkout". Some users have even not noticed that the order review did not contain their updates and proceeded anyway.
Note that this has been a historical issue with the cart, but can be resolved easily enough by attaching a Javascript event to the Review Order button that submits an asynchronous request to save the cart before moving on to the next step. This will have the same effect as clicking "Update Cart" without requiring additional explicit action from the user when they are already ready to make a purchase.