PDOException: SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry '1532856' for key 'PRIMARY': INSERT INTO {watchdog}
There are 2 things going on here. 


The PDOException is because Watchdog is trying to insert a duplicate primary key, 1532856. Your auto increment value could be off or some other table corruption could be going on there. A simple fix is to truncate the watchdog table if you don't care about maintaining old log data. Otherwise, you could try to repair the table or fix the auto increment value if you want to retain old log data. 
The error being logged has to do with your field-collection-item.tpl.php template in the Nexus theme on line 37. A key called field_enter_module_name_here is being referenced when it doesn't exist. It looks to be a custom template addition to the theme (it doesn't exist in the 7.x-1.3 release). Given, the key name, it sounds like some sort test code dropped into this template. This is warning so it shouldn't be a critical problem, but you should fix it to clean out extraneous errors from filling up your logs.