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.