obvious

It's enabled by default. Click the magnifying glass icon in the upper left area of the screen to reveal the form textfield.

Not that I would need to search the web to find an obvious element of the user interface... but really, OA, clicking to be able to type in the text box is a usability fail for something as important as search. The 15x50 pixels are available.

Order matters. condition() before countQuery()

This fails (note it trying to do a subquery):

<?php
return db_select('block')->countQuery()->condition('theme', $theme)->execute()->fetchField();
?>