I am having the same problem, particularly with type in tables. If I try to move the table or copy and paste it the type disappears from the table and I can not get it back. I have checked my fonts and nothing seems corrupt.
I have solved my problem for anyone else who encounters the same issue.
Locate the Adobe download assistant and look for InDesign, download InDesign and try installing it. Didn't work for me right away, but downloading it gave me the option to uninstall the program officially. Reinstalling it corrected all the issues and allowed my app manager to update it.
@benorose - Moved from the Creative Cloud to the InDesign forum. They will be able to help you here.
Branched this thread from http://forums.adobe.com/thread/1193152 thus the @AronBishop reply is out-of-context.
What do you see in Story Editor?