Yep there are actually quite a few plugins that have issues with WP 3.5. We got caught by surprise on this one. ;)
WP releases Nightly Builds and Beta versions of upcoming WP version releases that plugin authors can test with to ensure their plugins are working correctly with any new coding changes in each new version of WP that is scheduled for release. In the WP 3.5 release a last minute coding change was necessary and we were caught by surprise as many other plugin authors were as well. he he. ;)
Ok so this is what you should do to narrow down which plugin(s) or theme(s) might not be functioning correctly with WP 3.5.
Deactivate each plugin one by one and test things until you figure out where the issue is.
Then if it is not a plugin issue you will have to switch your theme to the WordPress 2012 theme briefly to see if it is your theme itself.
The CKEditor plugin is one of the plugins that is having a jQuery issue/conflict with WP 3.5 so if you are using that editor plugin then you will have to deactivate it for now until the plugin author can release a new verion.