TYPO3 Core

Here is a possible solution: Change the following lines in all JSManager Extensions that register any JS Libraries to JSManager extension:

if (!defined('TYPO3_MODE')) {
die('Access denied.');
}

require_once(t3lib_extMgm::extPath('extjs', 'class.tx_extjs.php'));
try {
tx_jsmanager_Manager::register(new tx_extjs());
} catch(Exception $e) {

}
?>

The error occurs because extjs is registered twice!

TYPO3 cannot check for all kinds of different extensions. Instead the extension should prevent such errors.

But as I read on the homepage of this extension, its function is already available in TYPO3 4.3 and newer by default.
See http://forge.typo3.org/projects/show/extension-jsmanager

Also the bug has been reported there
http://forge.typo3.org/issues/show/3422
but won't be fixed because of the reason above.