Show dialog at login (bash script)
You shouldn't need System Events just to display a dialog, nor can you strictly speaking 'activate' it...
try just 

#!/bin/bash
osascript &lt;&lt;EOD
  tell me to display dialog "Unauthorized Login" buttons {"OK"} default button 1 with icon caution with title "WARNING!"
EOD

echo "$(date) LogIn Alert" &gt;&gt; ~/Develop/login.log


I can't really test it as I'm totally clueless on cron/bash/osascript itself, but that would be all you'd need for a regular Applescript to display a dialog.

If that doesn't work, then the next step would be to set it up in Automator, as an Application, then set to launch at login.