Can Liquid Tape be used to touch up the rubber on the basket in my dishwasher?

Yes.  But, Liquid Tape is not recommended for use in dishwashers.  There are certain chemicals that are used in the Liquid Tape that you would most likely not wanting coming in contact with your dinnerware, glassware, silverware, and utensils.  GB does not offer anything that will work for this application.  There is a company called Plasti-dip, that offers a product that is specifically designed to use on repairing dishwasher racks.