If the title counts as a “mention”:
Pet Shop Boys, “Love Etc.”:
You need more
Than a big blank check to be a lover, or
A Gulfstream jet to fly you door to door
Somewhere chic on another shore
The Royal Guardsmen.
The song also mentions a shooting star. He may’ve meant the astronomical kind, but I think he was referring to the P-80 Shooting Star.
Like a G6 by Far East Movement
I posted the link to PP&M singing Early Morning Rain, and then @K364 posted Gordon Lightfoot (who wrote it). I was replying to him. 
From Oscar Brand’s ‘Wild Blue Yonder’ album:
I Wanted Wings: Zeros/Mitsubishis, Grumman [make, not specific], PBY, Grumman Duck.
Give Me Operations: P-38, P-39, P-40, F-86, F-84.
Wreck Of The Old 97: P-51.
I blame Monday, and having to head to the basement at midnight last night due to a tornado warning (and the resulting lack of sleep) for my lack of reading comprehension. Mea culpa.
Pink Floyd observed that a Lear Jet would be a desirable acquisition in ‘Money’.
If I was in the high-fidelity first class travelling set I might well make a similar purchase.
I’m going be pedantic and point out that Gulfstream is a manufacturer, not a specific model. A specific model would be something like a G6 (According to Wikipedia, they actually write it as GVI).
“Weird” Al Yankovic’s song “Airline Amy” chorus mentions a 747:
“You set my ever-lovin’ heart on fire, Airline Amy
Tell me I’m your favorite frequent flyer, Airline Amy
Found a little piece of heaven on a 747
And no one else can take me higher than Airline Amy”
Oh, and there was also an Aussie response/tribute song, “Sydney From a 727”.
Speaking of Lear Jets, Carly Simon also mentions in the “You’re so vain” song that the vain guy was ‘going to Nova Scotia to see the total eclipse of the sun’ in his Lear jet.
At the time the song was written, the specific model could have been a Learjet 23 (1962-1966), Learjet 24 (1966-1977), or Learjet 25 (1966-1982).
A lot of great examples so far, thanks!
I wonder if there are Airbus references? Maybe A320 doesn’t scan as well as 747.
It’s probably partly that, and no Airbus model has become as iconic as the 707 or 747, except maybe the A380. But like you say A380 really doesn’t scan very well.
The Seattle band Tagging Satellites had the song “DeHavilland Comet”.
The band, like the plane, is defunct.
Saxon - 747 (Strangers in the Night)
There’s a whole “Lear Jet Song” by the Byrds:
L.A. International Airport by Susan Raye. Perhaps you have heard of the place if not the song. She soars high above the heavens in a 747.