Although glitch seems a word that people would always have found useful, it is first recorded in English in 1962 in the writing of John Glenn:
Another term we adopted to describe some of our problems was "glitch".
Glenn then gives the technical sense of the word the astronauts had adopted:
Literally, a glitch is a spike or change in voltage in an electrical current.
It is easy to see why the astronauts, who were engaged in a highly technical endeavor, might have generalized a term from electronics to cover other technical problems. Since then glitch has passed beyond technical use and now covers a wide variety of malfunctions and mishaps.
Text: dictionary.com