Continuity mistake: Despite not having taken a sip from the champagne flute yet, the level in the glass when Lupin says "To my very own Marie Antoinette" is lower than the beginning (when he said "a cigarette saved my life"). (00:20:00)
Continuity mistake: Lupin expresses his last wish for a smoke, and as Nyx holds him at gunpoint asking if he has any trick concealed in the cigarette, pay attention to the left wall of the room and how part of the plaster is ruined and exposes the bricks underneath. In particular there's a smaller patch of bricks between the upturned table and the back wall. When later Nyx walks away, there is no such thing and that part of the wall has a much larger part where the plaster has been stripped off. (00:17:00 - 00:18:15)
Continuity mistake: When we first see Jigen on the cross, his shirt has one button left. They toss the bucket of water on him, and the shirt is now totally open. Later in the episode, when Lupin frees him, it's the other way around; the shot from the archway with the agent looking for Lupin shows Jigen in the background with the shirt open, but it's buttoned when his friend unlocks the shackle. (00:03:45)