Add (perhaps): Yaz - Goodbye '70s (released 1982)
And of course, Killing Joke - Eighties
Bruce Springsteen’s “My Hometown” states clearly that the narrator is 35 and was in high school in 1965. That places the song squarely in the mid Eighties.
“Hotel California” could be thought of as dated, or just out of wine for a really long time:
“We haven’t had that spirit here since 1969”
“American Pie” dates itself, though it never mentions the year explicitly.
Yeah, nine-deuce…Death Row records, creepin’ while ya sleepin’.
The Blues Brothers’ “Everybody Needs Somebody to Love” has an extended spiel by Dan Aykroyd: “Here it is, 1980, coming up on 1984.” I think it was actually performed in1978 and released in '79, though.
Mustang Sally by Wilson Pickett
“I bought you a brand new Mustang
A nineteen sixty-five
Now you come around
Signifyin’ a woman
That don’t wanna let me ride”
Not to mention the general stupidity of the line. Wine is NOT a spirit. It’s not distilled!
Hell, they had an entire album that was dated that way: Apocalypse '91: the Enemy Strikes Black. Still a great album, and very representative of its time, but wow.
“Black Stations/White Stations” by Martha & the Muffins:
Black stations, White stations break down the doors
stand up and face the music, this is 1984
Black stations, White stations feet on the floor
dance on the ceiling with us, this is 1984, Ha!
Well, at least that song’s got another 517 years before it becomes quaint, hokey and ridiculous.
Also Snoop.
“Nine trizzay’s the yizzear…”
Consider, too, the next line: “The disco hotspots hold no charms for you.”
“Look at Mother Nature on the run in the 1970s”/Neil Young, After the Goldrush
Not that the year is mentioned in the lyrics, but the title: Teenage Lament '74/Alice Cooper
Seven years later, Snoop Dogg again: “Nine-five plus four pennies! Add that s@#t up.”
Transplants, “Diamonds And Guns” (released in 2002):
"Yo, representin O-town 2002 Baby Transplants"
Didn’t Jefferson Starship have an almost identical line in “Ride the Tiger”?
ETA: Genesis: “Broadway Melody of 1974”
While it doesn’t mention a specific time, Joan Jett’s song “I love rock & roll” certainly has a dated reference…
“I love rock & roll,
Put another dime in the jukebox baby!”
When’s the last time you could play a jukebox tune for a dime?
I believe that when Ruben Studdard won American Idol, he put out a song that very clearly dated itself in 2004. And it also wasn’t very good, so two strikes against anyone remembering it. 
“She had a picture of a cowboy tattooed on her spine, saying ‘Phoenix, Arizone, 1949’”
Little Egypt by, I think, the Coasters