Software Updates show iLife Support 9.0.4

See my fix posted below.

I have the exact same problem!

Is there someone who can solve the problem?

Just before you click on the iLife download 9.0.4 go to your system preferences icon on the bottom bar or choose the black Apple icon in the left top of the desktop window -- click on one of these. Once open then click on the Security & Privacy icon, then go down to the bottom left of the pane and click on the gold lock to unlock it. You will need your system password. Next go to the iLife904 package and open it up. Then double click the iLife904.pkg file. You will get the message that you cannot install or open the file. Click on okay and the message goes away. Go back and look at your Security & Privacy pane and it should now say under the App Store and Identified Developers radio button, "iLifeSupport904.pkg" was blocked from operating because it is not from an identified developer. You will also see a button that says "Open Anyway" and you should click this button then the error pop-up message will return along with an an "Open" button. Click on the "Open" button and the "Welcome to the iLife Support Installer" pane opens and then click "Continue" and follow the prompts until fully "iLifeSupport904.pkg" is installed. After installation I recommend shutting down the computer to make sure the pre-boot files are saved correctly. Restart and you are done. No more System Preference with a Red 1 showing.

Just reinstall using pacifist after downloading the package from Apple website. After that the update goes away.