Other mistake: In every universe - except for the double-headed universe - Brian and Stewie travel to, they (seem to) replace the version of themselves that universe already has of them, but then in the Dog universe they have a separate version of themselves that they continuously interact with.
Continuity mistake: When Brian stops at the Marriott, he orders a Jack on the rocks. As he is ordering it, there is a woman in the background with a martini, then when the camera cuts to behind the counter when Brian receives the Jack on the rocks, the same woman has red wine instead of a martini.
Continuity mistake: During their lightsaber duel, Luke is holding his lightsaber when Vader cuts off his right hand, then Luke's hand and his lightsaber fall away so he loses both. However, after Luke is rescued by the Millennium Falcon, when the door opens as Lando helps an injured Luke, we can see the hilt of Luke's lightsaber hanging from his belt as he hugs Leia. (00:36:30 - 00:39:15)
Continuity mistake: After Fett takes off with Han frozen in carbonite C-3PO cracks a joke about rescuing him in three years. When it cuts to Vader with Luke, Vader uses the Force to break a pipe off the wall, and in the next wide shot Vader's chest plate is backwards, note the buttons. (00:35:10)
Continuity mistake: After Fett flies off with frozen Han it soon cuts to Vader and Luke during their lightsaber duel. When Luke is being pulled through the broken window he's holding his lightsaber in his right hand, then it disappears from his outstretched hand in the wide shot, but in the next closeup his lightsaber is suddenly clipped to his belt at his left side. (00:35:15)
Continuity mistake: Dak sits in the back of the snowspeeder and says "Right now, I feel like I could take on the whole empire myself" so Luke gets out. Dak is in back when he flies out but when he is in space he is now sitting in the front.
Continuity mistake: When Stewie goes down the stairs in his bed, when he hits the front door, the door opens outwards outside. It always opens towards the inside. Plus in this episode, the door is brown when he rolls outside. Next scene and the other times in the show it's a red door.
Continuity mistake: Chris puts a video recorder in his room to try to capture the angry monkey in his closet to show Peter and Lois. He views the tape the next day and sees Peter and Quagmire enter his room. Quagmire punches Chris in the eye and bruises, it but when we see Chris the very next day, there's no black eye.
Continuity mistake: In this episode, Lois is shown to have dated Naomi during college. But in the episode "Meet The Quagmires", it was established that Lois and Peter were already dating when Lois was eighteen. She accepted Peter's marriage proposal at that age. She would have been engaged and possibly married during college, not dating other people.