I have serveral domains (not a multisite setup) on the same server all running their own individual copies of wordpress 3.9.1 and content. I noticed that I was unable to add any tags, or set categories and those options disappeared from the “screen options” drop down. I started troubleshooting and disabled all plugins and switched to the default basic theme. Still didn’t work so I went as far as to repair the database, and even try adding define( 'CONCATENATE_SCRIPTS', false ); to the wp-config. That didn’t work either.
I then used one of my empty domains to do a brand new install of 3.9.1 and same problem!!
I figured out what the problem was. I had a function that was turning off the “heartbeat” apparently that was preventing the tags, categories and slug edits from occurring for some reason.