If you rely only on data passed by AJAX for page rendering your content will be invisible to search engines. That's it. According to this article preferred method to use AJAX is to start with classic refresh-per-click model that is visible to search engines then add Ajax scripting when applicable.
This week I have such situation when pure AJAX app was refactored for Google purposes. I discovered that initialisation of Dojo (that takes 3 seconds and above ten AJAX calls for *.js files) isn't very good thing if occurs every click. Didn't Dojo play well with apps that refresh page every request?
I found few interesting hints how this problem can be addressed and prepared custom Dojo build. It's working well and now initialisation of Dojo takes under one second (and it's acceptable now for end-user).