The new design for the special character tool is available here at mediawiki.org. You can test it by going to http://mediawiki.org/wiki/Project:Sandbox?veaction=edit and choosing the "Ω" button in the main toolbar.
This wiki (currently) only has a small, basic set of characters. The list can be expanded and customized at each wiki. Follow the instructions at VisualEditor/Special characters to add more characters. However, the method for customizing the tool will probably change during the coming months.
Please test this out and let the devs know what you think about it. Is this new, full-width tool better than the old floating palette in VisualEditor? How could it be improved?