How do I reject messages which were sent with an empty Mail From Header?
This filter is not recommended because most notification messages and some messages from mailing lists are sent with an empty Mail From.
To reject such messages you have to create a Content Filter which will match these messages.
Go to the Mail Service menu node -> Filtering -> Content Filters tab -> Add button. Choose the Where Sender Matches some words condition and Reject/Accept/Delete message action.

Click on some word link and choose RegEx (Regular Expression) in the Function pull-down menu. Now fill ^$ in the String text field (explanation - ^ denotes the start of the string and $ denotes the end so here you are looking for a string with nothing between the start and the finish, an empty string).

Confirm it by clicking OK. Reject action is chosen by default so you do not have to change that. Finish it by clicking OK again and the Close button and the filter will be set properly.
Tip 1: You can set the action to copy to email address so you can audit the rejected messages.