I try to keep everything clean. I hate the tactile feel of old dirt or mud still on discs from previous rounds. If it is really bad, a good wipe down from Acetone will remove almost any mark.
I have never thrown a bag in the wash or given them more than a quick wiping from a paper towel, but while playing I do my utmost to not get them dirty in the first place. As for leaves and grass inside the bag. I usually do not notice until it becomes too obnoxious or obvious.
As for my cart, yeah that will get wiped down almost immediately upon discovering something on it.
As for appearance in general. I try to run certain color schemes depending on the season. All white discs for the cart, unless white is not available in that plastic, in which case I substitute black in. For my Revo bag that I use more for the winter or for rounds that I will definitely have my camera with, I have an all yellow theme going. Finally, my Grip, which I use for recreational rounds I run a little more freely with my back-ups and practice discs, but mostly orange with some yellows.