The Man They Called a Magician - S1-E2
Continuity mistake: Pycal comes back home and finds only the ropes that he used to restrain Fujiko. The ropes are laid out differently between shots, and so is the position of his shadow over them. (00:12:10)
The Man They Called a Magician - S1-E2
Continuity mistake: When Pycal checks out Fujiko's recorded message, the distance between the tape player and the edge of the table changes between shots. (00:16:20)
The Man They Called a Magician - S1-E2
Other mistake: In his training at the end, Jigen shoots over a dozen times with his revolver without reloading. (00:21:20)
The Man They Called a Magician - S1-E2
Plot hole: Lupin was knocked out by Pycal when he shot him with a gun at point-blank. On the other hand, the 'shield' he used was strong enough to not even budge when Jigen's gun and several machine-gun shots would hit, and sustained the impact of an anti-tank rocket, so the dampening powers of the chemical are pretty inconsistent. It's also completely impossible that it works as shown, unless it also coats the mouth, the nostrils, the eyes.
The Man They Called a Magician - S1-E2
Other mistake: Despite falling unconscious at the bottom of the sea in his car and being rescued by Jigen, with Pycal within range since he got out of the car at the last moment, somehow Lupin gets to Pycal's home before he does, setting up a bunch of tricks in advance too.
The Man They Called a Magician - S1-E2
Other mistake: Lupin uses the three projectors to show Pycal the formula. To work, the projectors must carry one slide each, but then it turns out that Lupin had all three in hand the whole time.
The Man They Called a Magician - S1-E2
Continuity mistake: Pycal tortures Fujiko putting her through the trapdoor in her underwear, and pulls her up wearing a torn dress.
Farewell My Beloved Witch - S1-E3
Continuity mistake: Fujiko jumps on the bow to point the Walther P38 at the incoming speedboat, her foot is in a different position between shots - use the stripes at reference. (00:02:00)
Farewell My Beloved Witch - S1-E3
Audio problem: Lupin finds Linda in the flowerbed and eventually asks her what the flower known as 'Third sun' is. Her mouth starts moving, but the audio of the girl's answer comes with a significant delay. (00:08:20)
Farewell My Beloved Witch - S1-E3
Continuity mistake: When the professor demonstrates the power of the Third Sun, the hole in the floor has a regular, circular shape, but then it's smaller and irregular with large cracks around it. (00:09:35)
Farewell My Beloved Witch - S1-E3
Continuity mistake: When the professor crushes the flower under his fist, the flower suddenly grows an extra leaf at the cut. (00:10:25)
Farewell My Beloved Witch - S1-E3
Continuity mistake: When Lupin and Jigen approach Fujiko's burning plane, in the aerial shot the wreckage lost one of the blades, and the cart did a 180° turn. (00:12:50)
Farewell My Beloved Witch - S1-E3
Continuity mistake: When Lupin is sitting in the prison cell listening to Stern's proposal, he never moves but his butt still rests on a different spot almost each time - look at the tiles, and how sometimes he's precisely within a single one, other times he's between two. (00:15:00)
Farewell My Beloved Witch - S1-E3
Plot hole: Lupin was captured by chance, and he did not plan for that, nor he seemed to have previous knowledge of Stern's appearance, but he escapes regardless using a Mission Impossible-like perfect mask of him. He also somehow kept his own blazer, tie and shoes underneath the uniform and boots he stole and wore. (00:16:00)
Farewell My Beloved Witch - S1-E3
Other mistake: Lupin shoots a rocket from the plane, but in close-up you can see the flowers hit by a flamethrower stream. (00:17:45)
Farewell My Beloved Witch - S1-E3
Continuity mistake: The professor looks at the inferno burning in the field with or without putting the palm of his hands on the window, depending on the shot. (00:18:00)
Farewell My Beloved Witch - S1-E3
Continuity mistake: When Lupin cries out for Linda and opens the plane's door, he reaches out with his left hand, which becomes the right at the cut. (00:18:25)
Farewell My Beloved Witch - S1-E3
Continuity mistake: When Stern falls after Fujiko knocks him out cold, his beard is gone. (00:20:50)
Farewell My Beloved Witch - S1-E3
Revealing mistake: When Lupin is saved by Fujiko and is on the ladder, his lower left leg is missing. (00:21:05)
Farewell My Beloved Witch - S1-E3
Continuity mistake: When the missile emerges from the sea, it's plain dark grey; the remnants of it on the raft have recognizable multicolored paint. (00:22:05 - 00:22:50)