Please first disable the "System – System Restore Points" plugin, then install the updated version.
The System Restore Points has been removed over six months ago. It was removed before Joomla! 3.4 was released. Due to security changes in Joomla! 3.4.1 the System Restore Points feature is no longer compatible with Joomla! 3.4, hence the issue during the update.
If you're wondering exactly what is going on, the security change in Joomla! 3.4.1 was the inclusion of our contributed UploadShield code which scans uploaded (or downloaded over the web, e.g. from an update server) files for executable PHP code. When executable code is found it blocks the upload with the error message JLIB_FILESYSTEM_ERROR_WARNFS_ERR03. Since there are legitimate cases where executable code has to be uploaded –such as updating an extension– there is a way for developers to whitelist an upload action so that it doesn't go through filtering. This is what the System Restore Points feature doesn't do since that requirement came to be long after we had already removed this feature from our software.
Nicholas K. Dionysopoulos
Lead Developer and Director
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