Brought Home the Wrong Kid: In Blue Harvest, Peter mentions that he and Lois got halfway home with the afterbirth before going back to the hospital and swapping it out for Meg.
The Bus Came Back: One episode of the show had a running gag of a character who would constantly call Peter a phony. Despite being only in one episode, for one gag, nine years earlier, he was brought back for Something Something Something The Dark Side as Admiral Ozzel.
This is lampshaded by Stewie (as Vader) at the beginning of the third episode when Roger appears. Stewie is surprised and says something to the effect of "It's you [Roger]? Are we really out of our own characters? We have to use you?"
History Marches On: The DVD release of It's a Trap features a throwaway gag of Osama bin Laden popping up in the middle of the Tatooine desert to announce "Still alive!" Less than three weeks before the television premiere, this ceased to be so. The sequence was edited out of the televised version.
Imperial Stormtrooper Marksmanship Academy : In "Blue Harvest", when the group are fleeing the Death Star, no one is ever hit, even when Han (Peter) and Chewie (Brian) spend about 25 seconds standing at the doorway trying to get a couch through the door.
Incest Is Relative: The squicky implications of Leia's line that she "somehow always knew" Luke was her brother are discussed. She reveals that it's no big deal back on Alderaan, comparing it to the American deep south.
Mobile Fishbowl: In It's a Trap! Admiral Ackbar is a fish that pilots a robot body from a water filled globe at the head.
Motivational Lie: Subverted in Something, Something Dark Side. One Imperial soldiers asks what the rebels did that was so bad anyway, and Stewie claims that the rebels killed the dog of another crew member. It seems like an obvious lie, but later on Peter and Brian celebrate that time they killed that dog.
Princess Leia: Why, you stuck-up, half-witted, scruffy-looking nerf herder! Han Solo: Who's scruffy-looking?
And the scene in Something, Something, Something Dark Side:
Lois: Why, you stuck-up, half-witted, scruffy-looking nerf herder! Peter: *hits Lois* You can't use that word! Only we can use that word!
Peter: You my nerf-herder! Brian: No, you my nerf-herder!
May be a partly justified spoof, since it's canon within the Family Guy series that Peter has black ancestry. May have been a Callback to that fact.
Noodle Incident: Several, with three occurring in "Blue Harvest," both involving Obi-Wan/Old Man Herbert:
The first was in the scene where Obi Wan/Old Man Herbert receives the SOS signal from Princess Leia/Lois Griffin, where the latter mentions that (Obi-Wan) owes her for keeping several Alderaanian children silent for obviously sexual reasons, but the only thing we got out of her was "Joey Lawrence Haircut" due to Obi-Wan/Old Man Herbert fast forwarding through the details due to Luke Skywalker/Chris Griffin being nearby.
The second was when Darth Vader/Stewie Griffin encounters and duels Obi-Wan/Old Man Herbert, where it is mentioned that Vader/Stewie had placed a restraining order on Obi-Wan/Herbert with a distance limit of 50 yards for reasons unspecified.
Obi-Wan/Herbert also briefly mentioned something about sock puppets when telling Luke/Chris to use the Force to place the proton torpedos into the Death Star's thermal exhaust port that he entertained Luke/Chris with as a kid, but elaborates no further other than warning him not to mention the sock puppet shows because it would get him into trouble if he mentioned them.
No OSHA Compliance: The alarming lack of railings on the platform next to the Death Star planet-blower-upper gun is lampshaded.
The DVD commentary for "It's a Trap" mentions that Fisher was initially reluctant to voice for the special, but relented when she came to the conclusion that she'd be playing Angela and not Leia.
Before Mon Mothma shows up, this is lamp shaded in Obi-wan's reveal of Leia as Luke's sister: "Think about it. Who's the only damn woman in this whole freaking galaxy?!"
And as soon as Mon Mothma shows up, Leia immediately declares "I don't like her" before Mon Mothma even has a chance to say anything. Somehow, Leia is threatened by there being another person of her gender in the galaxy.
A giant one towards Fox in the text crawl of Something Something Something Dark Side, saying how the network that cancelled a lot of good shows in Seth's opinion didn't deserve the time and money it invests. Which it then furthered the point by interrupting the crawl to have a CG purple elephant waltz across the screen just to waste money.
Text Crawl: Wanna know how much that cost? $43,000. I'm not kidding, and it wasn't even funny. This is what Fox lets their money go to.
Also done at the end of It's a Trap! towards the series creator Seth McFarlane, by Chris, Lois, and Meg as revenge for Peter Griffin constantly ripping down Robot Chicken.
Some of the jokes in It's a Trap seem a little less...affectionate parody than the other two.
Peter: Did they braid your hair?
Lois: I know, it's not as good as Empire.
This Is Gonna Suck: At the beginning of "It's a Trap", the family doesn't seem so thrilled to be told Jedi.
Peter: (wearily) Let's just get through this.
Also done during the text crawl.
"You know what, we donít care. We were thinking of not even doing this one. Fox made us do it."
Written-In Infirmity: In-Universe example with Blue Harvest. Because Biggs Darklighter was portrayed by Joe Swanson, Biggs Darklighter was confined to a wheelchair. He explains that he got an injury from an accident regarding his repairing a Y-Wing that left him paralyzed.