Mac fails to restart/shutdown after installing update 10.11.6 - anyone with the same issue? Thanks

Reinstall El Capitan:

Reinstall El Capitan Without Erasing Drive

Please be sure you back up.

1. Restart the computer. Immediately after the chime hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the the side list.
4. Click on the First Aid icon in the toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Reinstall OS X and click on the Continue button.

Also, see this User Tip: Basic Steps for Upgrading OS X.

You can try shutting down the computer using the power button and then restart.