Star is very visual effect and like to see the things I have to do first marked with Star. However, the perfect behaviour will be all the task you need to accomplish today or task expired it would be STARRED by default and come to the firts places. At least, Star all the important task by time and it will be very fast to see.
Maybe changing colours depending the importance is other way to do it and get more visual the website and app.
Desing is a little outdated, seems Windows 95. Hope you are working to make more easy and pretty design.