Has the practice of women's head covering changed because customs change, while God's Word does not?
Yes. The practice of women's head covering has changed because customs and environment change, not because God's Word changes. Scripture remains authoritative, but the specific cultural application of head covering is treated as a custom-bound issue, so the verses are read with that distinction in mind.
Les teaches that women's head covering is an area that has certainly changed by virtue of customs and environment, not that the Word of God changes. He compares it to meat offered to idols, saying it is far removed from present-day America. He explains that God mandated many things for Israel because of their national customs and the way God had taught them. He does not take these verses as no longer being the Word of God, but says to take them with a grain of salt. He also notes a tremendous change in the position and attitude of men toward women in Christianity, and that Paul himself was not anti-woman.