We are not sure what caused the white damage on the tips. Lightly prune the damaged tips.
Right photo looks like yucca plant bug damage. These bugs are sucking insects. The leaves are stippled, have black fecal spots and eventually turn yellow. Prune out severely damaged leaves to the base.
You will have to look for the insects during the growing season. The adults have wings but do not fly readily, they are more likely to run when the plant is disturbed. Direct applications of Insecticidal Soap should provide control when you see the insects but must be repeated as needed. See our website for photos and more identification. http://extension.umd.edu/hgic/plant-bugs-flowers
Monitor your other yuccas during the growing season for signs of this insect and control as needed.