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Ringo and Fred pass through a room containing various pop-culture heroes, including John Steed, Mandrake The Magician and The Phantom. The latter also sort of a Mythology Gag as The Phantom, Mandrake and Yellow Submarine are copyrighted by King Features.
Fred: Can't we take one of these? Ringo: No, Fred, I only work with me mates.
The Sea of Monsters segment includes a parody of the then-current Hamlet cigar TV commercials (hence the incorporation of "Air on a G String" into the music at that point).
Several Beatles songs that weren't used directly in the film get referenced:
Fred: Won't you please, please help me? ("Help!")
Jeremy: Enough to fill the Albert Hall. (As part of a string of references on "A Day in the Life", one being that The Sea of Holes reminded John of Blackburn, Lancashire, to which Paul replies sing-songedly, "Oh, boy!")
Paul: Getting better all the time. ("Getting Better", obviously)
Pepperland John: I'm the alter ego, man. John: And I'm the ego man, goo goo g'joob. ("I Am the Walrus")
Lord Mayor: (to Old Fred) No time for trivialities. ("When I Get Home")
In the Gold Key Comics adaptation as the sub takes off with the Beatles and Old Fred in pursuit:
John: The sub is taking off without us.
George: You mean, 'within it, without us.'
Paul: This is no time to plug one of your songs! (a nod to George's "Within You, Without You")
This is followed by an encounter and wooing of a meter maid named Rita. ("Lovely Rita")
Then later, in the live action part:
Ringo: I've got a hole in my pocket! George: A hole? Ringo: Well, half a hole, anyway. I gave the rest to Jeremy! George: What can he do with half a hole? Paul: Fix it, to keep his mind from wondering! ("Fixing a Hole")
When the Beatles and Old Fred start to regress in age in the Sea Of Time:
Paul: Hey, Ringo, you're not half the man you used to be. ("Yesterday")
A couple of bars of "With A Little Help From My Friends" get played.
The frightening orchestra crescendo from "A Day in the Life" gets used for the start of the submarine's journey home.
In the opening sequence, when George is introduced, the opening of "Love You To" plays.
When the Beatles arrive in Pepperland, in order to "un-bonk" the Lord Mayor the four loop part of the lyric of "Think For Yourself".
When Ringo uses the hole in his pocket to break open the glass bowl imprisoning Sgt. Pepper's Lonely Hearts Club Band, the opening bars of "Baby, You're A Rich Man" play.
In the original cut of the movie, the boys sing half of the first verse.
George's catchphrase "It's all in the mind you know" is from The Goon Show (a suitable reference, as the Beatles really were fans of the Goons).
John says this a year earlier in The Beatles episode "Strawberry Fields."
The Apple Bonkers' Weapon of Choice look like the logo of a certain record company.
After the boys sing life back into Pepperland, the Chief croaks, "Hark...the hills are alive..." with Max replying in sing-song, "With the sound of music..."
The Boob, after he fixes the Sub's motor, quips "I must complete my bust, two novels, finish my blueprints, begin my Beguine." The last part refers to "Begin The Beguine," a 1935 song composed by Cole Porter.