I'm trying to test the new update on my test platform (j3.5.1, updated, not freshly installed).
I noticed that this file 3.6.0-2016-04-01.sql doesn't apply its changes in #__update_sites table in my database. Digging deeper I found out that this file refers to these names:
"Joomla! Core" and "Joomla! Extension Directory"
but in my case this table contains such names (without symbol "!"):
"Joomla Core" and "Joomla Extension Directory"
Sure sql cannot find these names and cannot apply.

Steps to reproduce the issue

Install Joomla 3.3.0 or earlier version.
Update to Joomla 3.5.1

Expected result

Go to database #__update_sites table
There should be "Joomla! Core" and "Joomla! Extension Directory" site names.

Actual result

In fact, the names are without symbol "!".
So we get an obvious difference between updated Joomla and freshly installed Joomla.
Because of this 3.6.0-2016-04-01.sql cannot be applied.

Additional comments

Exploring the problem I discovered when this inconsistency was made.
In Joomla 3.3.1 installation joomla.sql file contains:

INSERT INTO `#__update_sites` (`update_site_id`, `name`, `type`, `location`, `enabled`, `last_check_timestamp`) VALUES
(1, 'Joomla Core', 'collection', 'http://update.joomla.org/core/list.xml', 1, 0),
(2, 'Joomla Extension Directory', 'collection', 'http://update.joomla.org/jed/list.xml', 1, 0),
(3, 'Accredited Joomla! Translations', 'collection', 'http://update.joomla.org/language/translationlist_3.xml', 1, 0);

In Joomla 3.3.3 installation joomla.sql file contains:

INSERT INTO `#__update_sites` (`update_site_id`, `name`, `type`, `location`, `enabled`, `last_check_timestamp`) VALUES
(1, 'Joomla! Core', 'collection', 'http://update.joomla.org/core/list.xml', 1, 0),
(2, 'Joomla! Extension Directory', 'collection', 'http://update.joomla.org/jed/list.xml', 1, 0),
(3, 'Accredited Joomla! Translations', 'collection', 'http://update.joomla.org/language/translationlist_3.xml', 1, 0);

As you see, exclamation mark has appeared, but only for freshly installed Joomla.
But how about those site that update their Joomla? These names were never renamed.