The black squares even happen in phpMyAdmin - not when looking at text in tables, but actually in the phpMyAdmin strings like "Loading...", suggesting this is a low-level configuration problem.
I've read about this here and elsewhere and tried several remedies, all to no effect.
It's happening on a new VPS: Debian/Apache 2.4.10/MySQL 5.6/php 7.
Server connection collation: utf_general_ci
php_info() shows default_charset: UTF-8
php version is 7.0.20-1~dotdeb+8.1
page headers show Content-Type text/html; charset=iso-utf-8
there is no meta charset in the HTML
Apache mime module is active
The squares are occurring for characters like ellipsis, emdash, etc.
Any thoughts?