Joomla! module assignment list is broken
If the module selection list in the module assignment is broken, i.e. the tool for select / deselect of sub menu items is missing and the layout is generally garbled, the cause can be a menu item in the menu above that is listed as a child item but has no parent.
Go the the menu items for the last menu that is working. A menu item which has a missing parent has one or more leading vertical bars before the menu item name (instead of the leading dash which is the normal indication of a child item).
Just open the menu item and save it.