1. The page cannot be bookmarked 2. If java script is disabled , Ajax will not work 3.Because different components of the pages are loaded at different times, response time may be slow. 4.Because different components of the pages are loaded at different times it may create confusion for the user.
I find that like any other protocol, Ajax works best in tightly controlled conditions. It wouldn't make much sense for updating nearly the whole page, unless you find that the user experience is improved with an on-page 'loader'. Without going into workarounds, disadvantages will include losing the browser back button / history, issues such as the one your friend mentioned, and also embedded resources and other rich content can suffer as well, and just having an extra layer of complexity to deal with in your app. Don't treat it as magic sauce for your app - make sure every use delivers specific results that benefit your client / audience.
There are some limitation of AJAX which are as follows : 1. It is difficult to bookmark a particular stage of an application. 2. Function provided in code behind file does not work , Because the dynamic page cannot register themselves on browser history engine automatically. 3. If JavaScript is disabled then AJAX not able to perform any task. 4. Response time may be slow because different controls of page are loaded at different time.