Hello, Jeffrey,
I, too, encountered the same warning (Warning: unserialize() expects parameter 1 to be string, array given in /home/content/p3pnexwpnas12_data03/05/3640305/html/wp-content/plugins/widget-options/core/functions.option.tabs.php on line 30) after installing Widget Options on a site running WP 4.6.1, theme GeneratePress, with an assortment of other plugins (list on request). The warning did NOT appear while I was configuring and testing the site while logged in (in Firefox) as an administrator, but DID appear when I viewed the site without logging in, using Safari and Chrome. Logging out of Firefox caused the warning to appear there, too.
I’ve replaced the functions.widget.display.php file on the site with the development version in your reply, and the error no longer displays on the home page, however unfortunately show/hide doesn’t appear to work (all three widgets in the right sidebar on the home page appear although the Search and Archive widgets are supposed to be hidden), and the warning for unserialized() appears on the Blog page.
I’m not seeing the same issues on a test site which also uses WP 4.6.1 and GeneratePress, and the same set of plug-ins but a lot less content.