Index: src/wp-admin/js/customize-nav-menus.js
===================================================================
--- src/wp-admin/js/customize-nav-menus.js	(revision 34830)
+++ src/wp-admin/js/customize-nav-menus.js	(working copy)
@@ -1871,6 +1871,9 @@

 					control.isSorting = false;

+					// Reset horizontal scroll position when done dragging.
+					control.$sectionContent.scrollLeft( 0 );
+
 					_.each( menuItemContainerIds, function( menuItemContainerId ) {
 						var menuItemId, menuItemControl, matches;
 						matches = menuItemContainerId.match( /^customize-control-nav_menu_item-(-?\d+)$/, '' );