Noted in a Russell Baker column from 1965:
"Observer: America's New Class System"
New York Times, Apr. 11, 1965, p. E14
Your teen-age daughter asks what you think of her "shades," which you are canny enough to know are her sunglasses, and you say, "Cool," and she says, "Oh, Dad, what a spaz!" (Translation: "You're strictly from 23-skidoo.")
This is of interest for those familiar with the Areffian history of "cool" (1), wherein 1965 represents something of a nadir. Baker's daughter (we assume it's his daughter, despite the second-person narrative) clearly thinks that Dad is uncool for using the word "cool". It would be a decade before "cool" was cool again.
The other notable usage in the above quote is "spaz". The OED has another 1965 cite for "spaz" from movie critic Pauline Kael:
1965 P. KAEL I lost it at Movies III. 259 The term that Americanteen-agers now use as the opposite of 'tough' is 'spaz'. A spaz is a person who is courteous to teachers, plans for a career..and believes in official values. A spaz is something like what adults still call a square.
Pre-1965 examples of "spaz" are difficult to find in print (though the new OED draft entry for the verb "spaz" includes an example from 1957). Like the longer form "spastic", it was (and is) considered to be an offensive epithet. As Robert Burchfield noted in the OED2 entry for "spastic" (meaning "one who is uncoordinated or incompetent; a fool"), "it is generally condemned as a tasteless expression, and is not common in print." But once "spaz" developed into the 'uncool' sense as above, it was apparently distant enough from "spastic" to make it into print.
The earliest public attestation I know of for the 'uncoordinated' sense of "spaz" is the undeniably tasteless garage-rock single "Spazz" by the Elastik Band (Atco #6537, Nov. 1967), included in the box set Nuggets: Original Artyfacts from the First Psychedelic Era 1965-1968 (2). The catchy refrain goes, "I said, get offa the floor, get offa the floor, boy, people gonna think, yes they're gonna think, people gonna think you're a spazz." (This is also the earliest example I know of for the double-z spelling of "spazz".)
(1) See helpful graph here:
http://groups-beta.google.com/group/alt.usage.english/msg/3f06c74c4c3ef4e3?dmode=source (2) The single is described here: