In short, clicking on “Place Block” results in a brief loading icon and then nothing, and Configure Block results in a “This website encountered an unexpected error” message. The fix was found here:
https://www.drupal.org/node/2597506
Edit the following file – the “core” directory should be in your Drupal 8 root directory:
[drupal root]/core/lib/Drupal/Core/Annotation/Translation.php
Before the final }, add the following text:
public function __toString() {
return $this->translation->__toString();
}
Now try placing a block again and it should work. Please note that until this change is added to the Drupal code this is probably going to revert when you upgrade Drupal.