I think a disposable broom would be useful in the instance you are cleaning something up that you would make you not want to use your broom again after the mess up (i.e. vomit with the sawdust stuff on it - it happened today in my classroom). Just threw the broom away! If there was a disposable broom for this or oil spills sopped up with cat litter on them, etc. then it could be used to clean the mess up and not contaminate your regular broom.
They make disposable toilet seat covers so why not disposable shopping cart handle covers? Same idea similar material. Just to keep the germs away especially during cold and flu season.
Some sort of litter catcher would be nice. I have bought mats, covered boxes, and everything else, but some how there is always litter all around the litter box. If there was some product out there that helped to keep the litter in the box and not all over the floor that would be helpful. Or maybe change the litter so it isn't as easily spread all over the floor.