When you animadvert upon something, you criticize it openly and harshly. A high school debater might animadvert on the subject of the death penalty, for example.
The verb animadvert is a great word to use when you need a formal way to talk about a public condemnation of something or someone. A tourist might animadvert upon the entire country of Italy after a disappointing vacation there, or a politician might take advantage of a public forum to animadvert on the issue of high taxes. The Latin root word is animadvertere, "to notice or take cognizance of," or "to censure, blame, or punish."