WordPress 3.9 does not use the “wpdialogs” TinyMCE plugin as part of the TinyMCE 4.0 update ( #16284, #24067), which comes with a new dialog manager. (For more, see this post and their migration guide.) This was a jQuery UI wrapper we had introduced back in WP 3.1. If you were using this in your own scripts, please be sure you are setting “wpdialogs” as a script dependency.
If you were using jQuery UI for anything on the post screen, please be sure you are setting this as a script dependency.
In both cases you may need to enqueue the “wp-jquery-ui-dialog” stylesheet, if you are using the WP UI dialog design.