Q: Notes refuses to close and steals focus within seconds of closing

Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later.

Isolating an issue by using another user account

If the problem is still there, try booting into the Safe Mode.  Shut down the computer and then power it back up. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application unistaller. For each disable/delete, you will need to restart if you don't do them all at once.

Safe Mode

Safe Mode - About

General information.

Isolating issues in Mac OS X

Troubleshooting Permission Issues

Step by Step to Fix Your Mac

Try the Safe Mode as it resets things in your user account.

If you're synchronizing Notes with iCloud or another server, disable that and see whether there's any change.