What kinds of things does Deuteronomy 27 list that bring down the wrath of God?
The supplied context does not enumerate the specific deeds in Deuteronomy 27; it only says that chapter catalogs the horrible things mankind can do which bring down God's wrath. The discussion ties these to being under the works of the Law and therefore under the curse, which Paul references in Galatians.
Les explains that Deuteronomy 27 is the chapter Paul refers to in Galatians when he writes that as many as are under the works of the law are under the curse. According to the transcript, Deuteronomy 27 comes through all the horrible things mankind can do which bring down the wrath of God, but Les does not examine every one of them; he says they will not look at all of them and just come down to that chapter. The broader point is that people can think they are law keepers and commandment keepers, pleasing God, while actually placing themselves under the curse.