Why does Vladimir/Mr. Scruffles and his fellow lab rats want revenge of Mrs. Wakeman? Because she altered their bodies to resemble Mickey Mouse. And at the end of their debut, Wakeman holds up a familiar pair of pants for Vladimir to wear...
That whole episode was an allegory of the Soviet revolution; the leader's name is Vladimir, he speaks in a Russian accent, calls his fellow rats his "comrades", there's a Russian-style music score throughout the episode, and there's even a hammer and sickle in the episode's title card.
The male half of the alien couple in "Unlicensed Flying Object" sneaks one in.
Alien: Yeah, well, personally I can't wait to get off this hick planet! Bunch of rip-off artists, these earthlings: five bucks for a cup of coffee, no Extraterrestrial discount at the hotel, and I know that bellboy stole my tricorder.
In "The Puppet Bride", the boy that eventually finds Little Acorn looks identical to Lucas from MOTHER 3.
That episode is also based on the original story of Frankenstein.
In one episode, Tuck calls Dr. Wakeman to get Jenny and Brad in trouble for throwing a party while she is away. When Brad decides to let him stay for the party, Tuck responds to Dr. Wakeman's "Hello?" with, "I just called to say I love you."
When Jenny's identity is outed on Cluster Prime, a robot points at her, drops its jaw, and starts shrieking in a similar manner to Donald Sutherland in Invasion of the Body Snatchers.
Sheldon and Nora argue and eventually brawl over their techniques in getting to Cluster Prime, causing each of their machines to topple into each other, resulting in an exchange worthy of a Reese's Peanut Butter Cup commercial.
Nora:Hey! You got your time fissure capsule in my quantum defibulator!
Sheldon: You got your quantum defibulator in my time fissure capsule!
[The machines activate and open a portal to Cluster Prime]
Sheldon: Two great machines...
Nora: ...that work great together!
After Brad finds out that Melody is a robot, he asks how he can trust her again, and she kisses him. His response: "So she's mechanical!"
One to John Carpenter's The Thing (1982) of all ...things, in "Toying with Jenny." After Tuck tears the head off of one of the dolls, it produces four spider-like legs from its neck and walks away.
In the beginning of "Killgore", the toy store manager calls him Kilroy.
Sheldon's training sequence in "Agent Double-O Sheldon" spoofs J's in Men in Black.
When Jenny passes through a convention in "Infectious Personality", one of the con-goers wears a cardboard box over his head with a downward-facing arrow on the front, which looks a lot like an airbending tatoo.
In the pilot Jenny eats an ice cream cone, only to open her stomach and take it out, much like Astro Boy.