The story is a courtroom drama. It opens in 2033, with Simon Ninheimer, a professor of sociology, suing US Robots for loss of professional reputation. He contends that robot EZ-27 (aka "Easy"), whilst leased to Northeastern University for use as a proofreader, deliberately altered and rewrote parts of his book Social Tensions Involved in Space Flight and their Resolution whilst checking the galley proofs (hence the title). Ninheimer holds that the alterations to his book make him appear an incompetent scholar who has misrepresented the work of his professional colleagues in fields such as criminal justice in absurd ways.
Susan Calvin (US Robots Chief Robopsychologist) is convinced that the robot could not have acted as Ninheimer claims and that it was ordered to do so, but infers from its refusal to answer questions about the matter that it has been ordered into silence by Ninheimer. In any case, a robot's testimony in its own defence is not legally admissible as evidence. During the trial, Ninheimer is called as a witness for the defence in the presence of EZ-27 and tricked into lifting EZ-27's inhibition on accounting for its actions. He responds to robot's intervention by angrily denouncing its disobedience to his order to remain silent, thus implicitly confessing to having attempted to pervert the course of justice.
The story's final scene consists in the post-trial encounter between Ninheimer and Calvin in which Ninheimer explains his attempt to frame EZ-27 in order to bring disgrace on US Robots. He was motivated by his fear that the automation of academic work would destroy the dignity of scholarship and argues that EZ-27 is a harbinger of a world in which a scholar would be left with only a barren choice as to what orders he should issue to robot researchers