This below files are stored in the compilation folder 

\public_html\includes\src\Mage_AdminNotification_Model_Feed.php, \public_html\includes\src\Mage_AdminNotification_Model_Observer.php, \public_html\includes\src\MSP_Common_Model_Feed.php

So first navigate to magento root >> includes >> config.php and comment both below lines in this config.php file.

    #define('COMPILER_INCLUDE_PATH', dirname(__FILE__).DIRECTORY_SEPARATOR.'src');
    #define('COMPILER_COLLECT_PATH', dirname(__FILE__).DIRECTORY_SEPARATOR.'stat');

Than after clear the cache and again do the compile form the admin.