Tags and media can't be added after upgrading to WP 3.9.1

Have you tried:

– switching to the default theme to rule out any theme-specific problems.

– resetting the plugins folder by FTP or PhpMyAdmin. Sometimes, an apparently inactive plugin can still cause problems.

– re-uploading all files & folders – except the wp-content folder and wp-config.php & root .htaccess files – from a fresh download of WordPress. Make sure that you delete the old copies of files & folder before uploading the new ones.