I don't have due dates on a lot of my stuff, but I do have a rotating/constantly changing set of prioritized items. I would love to be able to set those up (whether in one board or several) and have them be at the top of my home ... and have me be able to prioritize them so they would show in the most important to least. And I could change a cards priority.
Labels allow for something like this, but that seems to affect filters more than anything. I want easy lists of "here's what you are doing now" kind of things.