In the TOS episode Court Martial,
Wikipedia summary: Captain Kirk is placed on trial for negligence after a crewman is killed during a severe ion storm. Kirk maintains that his actions were proper and should not have led to the officer's death, but the evidence seems strong against him. Will Kirk's crew be able to save the captain from conviction?
Spock's third-act new evidence was rather slim:
Wikipedia plot: ... Spock, noting he has been able to beat it at chess four times and was well on his way to a fifth, reveals that his "leisurely" activity was in fact an investigation of a computer that had told an account of the incident that, as an eyewitness, he absolutely knew was false. His victories had come despite the fact that Spock was the one who wrote the computer's chess program and the machine should therefore be incapable of doing any worse than a draw; when McCoy asks how that is possible, Spock explains he is convinced that the system has somehow been tampered with since game programming he made three months before has now been altered.
Really? No protected memory? Altering the logs affects the game AI? Is this really supportable, even from the POV of 1969 computers?