Wasn’t the cost of a phone at the time of the song already quarter? And that he ended the song with you can keep the dime just because it sounded better?
I was thinking of this song for this thread, as well. The concept of getting help from an operator to place a call, as well as the “you can keep the dime” reference to a pay phone, are, at best, anachronistic now, if not completely lost on younger listeners.
Good question. I suspect the whole USA didn’t switch from dimes to quarters overnight.
I can recall feeding a dime into a payphone to call home at least a time or three, and in 1972 I was 13 turning 14 and of course not yet driving. So there’s a rather narrow window of years where I’d be old enough to be out in retail public on my own without adult oversight, but dimes were still in use if by 1972 quarters were the going price. I was living in SoCal, which was / is a rather expensive area overall, so likely to be one of the earlier areas to switch from dimes to quarters.
In My Merry Oldsmobile
I suspect that this may have been the case, especially as it rhymed with “thank you for your time” (and slant-rhymes with “you’ve been so much more than kind”).
Ok, now that brings up an (evil) tangent: words that rhyme or mostly rhyme with “quarter”. Sounds like a category on Jeopardy that will get played last and only in desperation.
Sylvia’s Mother has a similar pay phone reference:
And the operator says 40 cents more
For the next three minutes
Definitely a dime. From Wikipedia:
On average, payphone calls generally cost 5¢ into the 1950s and 10¢ until the mid-1980s. Rates standardized at 25¢ during the mid-1980s to early 1990s. The Bell System was required to apply for increases through state public service commissions. Therefore, the actual increases took effect at different times in different locations
Do you want dated? Do you want fairly obscure?
I give you “Foreign Object” by The Mountain Goats.
Whipped like a dog, down on the cards
Square in the spotlight sweating real hard
All soaked in blood like a newborn babe
Sharp thing hidden in my hand shaped like an astrolabe
I still use the phrase dropped a dime on someone, even though it’s as ridiculous as telling people to dial xxx-xxx-xxxx.
Whenever I think of obsolete tech in songs, I think of “2-Way Freak” by Three6 Mafia. Here’s the lyrics but I’ll spoiler the link as the words are NSFW (written lyrics, not a video).
Summary
The song is about getting a ton of pages from women on their two-way pagers (different from a regular pager), but also the women scrolling through their pagers to see who they’ve been in communication with.
Two-way pagers were expensive (much more than a conventional one-way pager) and I don’t think they were very widely used. Here’s an article with more info on two-ways. It says they were introduced in 1995 and Motorola discontinued theirs in 2001. But they are still used for doctors!
There’s also
Which includes a reference to a “deuce” meaning a particular year and model of car from 40+ years ago then and 90 years ago now. If you weren’t a car nut then you’d probably have no idea what they were talking about.
With bonus points for apparently being one of those often misheard lyrics where various folks’ ideas of what they’re singing are all over the map.
You win. We’re done here. The rest of us don’t stand a chance of topping that. 
eh forget it
Another pager one is Crazy in Love by Beyonce (got me hopin’ you’ll page me right now") released in 2003, although pagers were on the way out by then.
In the song I Don’t Like Mondays by The Boomtown Rats is this verse:
The Telex machine is kept so clean
And it types to a waiting world
And there’s Pocket Calculator by Kraftwerk.
“Video Killed the Radio Star” is now a song about two obsolete music formats.
Huh? I still watch music videos on YouTube and listen to songs in my car on the radio. And I wish I still had my vinyl record collection.
A few:
“Telephone Line” - ELO
“Little Deuce Coupe” - Jan And Dean
“Kodachrome” - Paul Simon