What's the power of entertainment industry according to Barthes, Freud and Adorno?
I would start my answer by pointing out that you're dealing with three thinkers belonging to different time periods. Freud's psychoanalysis was one of the sources of inspiration for Adorno and the Frankfurt School in the 1920s and 1930s, the others being Weber's suspicion of rationality and Marx's ideology. Freud's idea that the social order works through pyschic obliteration and his notion of the unconscious were influential in the critique of society produced by Adorno and other members of the Frankfurt School, including their criticism of the culture industries. In Dialectics of Enlightenment, Adorno denounces the power of the entertainment industry to manipulate its consumers and make them passive, rather than critical observers. In this way, the entertainment industry becomes a dangerous tool of propaganda for totalitarian regimes.
In Mythologies, Barthes too commented on popular culture as a "myth" which can work to legitimize bourgeois ideology as natural. As in the critique of the Frankfurt School, Barthes finds that the mythologies of mass culture can pass off their representations of reality as the reality itself. Modernist art, on the contrary, can resist this totalizing claim by making the reader/spectator an active producer of the text's meaning.