The back of mouth, the soft palate, is yellow. Is this bad? What should I do?

Don't worry. Though we are always concerned about tissue color changes, I do not think that if seems too alarming. This broad area of yellow is most likely stain from food, drink, medication or tobacco. No other signs or symptoms but you can see your dentist to be sure.
See below. First do you have any other symptoms? What color is your tongue? This is usually seen with a tongue that is yellowish or yellowish/green and is indicative of liver or gall bladder i nvolvement buty if this is just on your palate i would see a physician.