I'm not sure why you would get this error. I can tell you that the problem is most likely the double ' around the following:
1
0000-00-00 00
0000-00-00 00
I also know that when I go and look at /setup/inc/osticket-v1.6.sql that I do not see two ' around these values (i.e. ''1'' and ''0000-00-00 00'' etc.) Note that this is not a double quote (") your cut and paste is two single quotes (').
Here is the pertinent code in the distribution:
DROP TABLE IF EXISTS `%TABLE_PREFIX%api_key`;
CREATE TABLE `%TABLE_PREFIX%api_key` (
`id` int(10) unsigned NOT NULL auto_increment,
`isactive` tinyint(1) NOT NULL default '1',
`ipaddr` varchar(16) NOT NULL,
`apikey` varchar(255) NOT NULL,
`updated` datetime NOT NULL default '0000-00-00 00',
`created` datetime NOT NULL default '0000-00-00 00',
PRIMARY KEY (`id`),
UNIQUE KEY `ipaddr` (`ipaddr`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8;
You can probably change the values to double quotes (") and not have any issues so long as you to not change the back ticks (`) around the column names. The code in your error log works for me if I swap the quotes as noted.