Coming Home - S1-E13
Continuity mistake: Sayla and Mirai are chillin' on the beach, sunbathing. They even comment on the sun and how light comes from just one direction as opposed to what they are used to in space and the colonies. Kai with his boombox passes them by asking about Amuro, and suddenly they both (Mirai in particular, under the parasol) have big shadows over them. (00:02:45)
Coming Home - S1-E13
Continuity mistake: Amuro looking from the window sees 4 drunk soldiers in his living room. Two of them tumble on the ground, where items like a helmet, a plate and empty liquor bottles lay around. One of the soldiers even has a bottle in his left hand he is still drinking from after the fall. When he enters the room and turns the radio off, all those items have disappeared. (00:04:20)
Coming Home - S1-E13
Continuity mistake: When the Zeon soldier enters the refugee camp structure, looks around and starts questioning the kid, the people in the background change from shot to shot. (00:13:50)