A “glitch” is problem (such as a computer “bug”), usually involving technology. The Oxford English Dictionary states “etymology unknown.” Merriam-Webster and the Wiktionary speculate that it’s probably from the Yiddish word glitsch, meaning “slippery.”
   
“When the radio talkers make a little mistake in diction they call it a ‘fluff,’ and when they make a bad one they call it a ‘glitch,’ and I love it” was cited in print in 1940 (and discovered by the American Dialect Society’s Fred Shapiro). The word “glitch” moved from radio in the 1940s to television in the 1950s and to computing and the space program in the 1960s.
 
In October 2013, the failure of the Patient Protection and Affordable Care Act (“Obamacare”) website was blamed on “glitches.”
 
 
Wiktionary: glitch
Etymology
Probably from Yiddish גליטש (glitsch), from dialectical German glitschig (“slippy”), from glitsch (“slide, glide, slip”) + -ig (“-y”). Related to gleiten (“glide”).
Popularized 1960s, by US space program. Attested 1962 by American astronaut John Glenn, in reference to spikes in electrical current.
Noun
glitch (plural glitches)
1. A problem affecting function; a bug; an imperfection; a quirk
2. (video games) A bug or an exploit.
 
(Oxford English Dictionary)
glitch, n.
Pronunciation:  /ɡlɪtʃ/
Etymology:  Etymology unknown.
Astronauts’ slang. A hitch or snag; a malfunction.
1962   J. Glenn in Into Orbit 86   Another term we adopted to describe some of our problems was ‘glitch’. Literally, a glitch is a spike or change in voltage in an electrical circuit which takes place when the circuit suddenly has a new load put on it… A glitch..is such a minute change in voltage that no fuse could protect against it.
1962   J. Glenn in Into Orbit 245   Glitch, a momentary change in voltage in an electrical circuit; (slang—a hitch).
 
glitch, v.
Etymology:  Apparently <

glitch n.
colloq. (orig. U.S.)
intr. To experience a glitch, setback, or malfunction; to go wrong. Also occas. trans.: to cause (something) to experience a glitch.
1962   Washington Post 14 Oct. 1/1   We’ve gone almost 55 hours..and we haven’t glitched (met unexpected problems) yet.
     
19 May 1940, San Diego (CA) Union, “Out of My Mind” by Katharine Brush, pg. 8-C, col. 3:
GLITCH PLEASES
When the radio talkers make a little mistake in diction they call it a “fluff,” and when they make a bad one they call it a “glitch,” and I love it.
 
Google Books
Mikes Don’t Bite
By Helen Johnson Sioussat
New York, NY: L. B. Fischer
1943
Pg. 216:
Pull a beard—Mispronounce a word; an accidental slip of the tongue. Also called “muff,” “fluff,” “bust,” or “glitch.”
 
Old Fulton NY Post Cards
30 July 1945, Long Island (NY) Daily Press, “Listen Here! Radio Has Its Own Jargon” by Dell Chandler, pg. 18, col. 2:
PULLED A BEARD—A muff, a fluff, bust, or glitch—in other words, a mispronounced word.
 
Google Books
The Advertising and Business Side of Radio
By Ned Midgley
New York, NY: Prentice-Hall
1948
Pg. 278:
Usually most “glitches,” as on-the-air mistakes are called, can be traced to a mistake on the part of the traffic department.
 
Google Books
15 October 1955, The Billboard, pg. 4, col. 1 ad:
They talk of Pigeons and Glitch
“Pigeons” are not birds to a Bell System technician. They are impulse noises causing spots which seem to fly across the TV picture. And when he talks of “glitch” with a fellow technician, he means a low frequency interference which appears as a narrow horizontal bar moving vertically through the picture….
BELL TELEPHONE SYSTEM
   
Google Books
Datamation
1960
Pg. 98:
A statement like, “Joe Glitch is a fat-head!” can be dangerous. Glitch might shoot you; or, at least, sue you.
 
18 April 1964, San Antonio (TX) Express-News, “‘Sick bird wit a glitch’: How To Talk ‘Rocket’” by Stephen Trumbull (World Book Encyclopedia Science Service, Inc.), pg. 11A, col. 3:
A “glitch” is an unidentified failure somewhere in the complicated mechanism—somewhat similar to “gremlins” which created difficulties for the early aviators.
 
9 June 1965, Boston (MA) Herald, “Marge” by Marjorie Mills, pg. 38, col. 1:
One of the scientists gave us a dandy new slang phrase when the computer failed…“It was a GLITCH.”...MUCH better word than “goof.”
   
Google Books
Data Processing Digest
Volume 13
1967
Pg. 34:
It was in the pages of CN (Computing News.—ed.) that Doctor Stoerben von Hunger popularized the terms kludge and glitch, which are today a standard part of every technical person’s vocabulary.
 
OCLC WorldCat record
13’s Glitch, 14’s Delay
Edition/Format: Article Article : English
Publication: Science News, v97 n24 (Jun. 13, 1970): 571
Database: JSTOR Life Sciences Collection
 
Google Books
What’s the Good Word?
By William Safire
New York, NY: HarperCollins
1983
Pg. 90:
The first time I (Tony Randall—ed.) heard the word “glitch” was in 1941 in Worcester. I got a job there as an announcer at WTAG. When an announcer made a mistake, such as putting on the wrong record or reading the wrong commercial, anything technical, or anything concerning the sales department, that was called a “glitch” and had to be entered on the Glitch Sheet, which was a mimeographed form. The older announcers told me the term had been used as long as they could remember.
 
NPR—All Tech Considered
What’s A ‘Glitch,’ Anyway? A Brief Linguistic History
by EMILY SINER
October 24, 2013 7:01 AM
HealthCare.gov, the faulty website where people can sign up for health insurance under the Affordable Care Act, has become nearly synonymous with the word “glitch” — sometimes defensively, sometimes mockingly.
(...)
Astronaut John Glenn used the word in his 1962 book, Into Orbit: “Another term we adopted to describe some of our problems was ‘glitch’. Literally, a glitch ... is such a minute change in voltage that no fuse could protect against it.”
 
In 1965, The St. Petersburg Times reported that a glitch (“as technicians call such abnormalities,” it clarified) had altered the computer memory inside the U.S. spacecraft Gemini 6. Six years later, The Miami News talked about a failure in Apollo 14 that almost prevented a successful moon landing:
   
Visual Thesaurus
The Hidden History of “Glitch”
November 4, 2013
By Ben Zimmer
(...)
Though we still don’t know for sure if the term was imported via Yiddish or came directly from German, a Yiddish origin certainly seems more likely. I’m not aware of any evidence of its use in historically German-speaking regions in the U.S., and its emergence in radio circa 1940 is telling, given the active role of Yiddish speakers in the world of radio at the time.