The Left Hand of the Magician - S1-E5
Plot hole: Luca draws the sketches of a magic trick, but they contain a fatal flaw that would kill whoever is doing it. He is hospitalized so he takes no part in the setup, so there is basically no chance that the flaw would go undetected. Other people are building the stage and device and they'd do at least a couple of tests before debuting a death defying stunt with live arrows and fire during the show.
The Left Hand of the Magician - S1-E5
Plot hole: Luca is the one who set a deadly trap, but somehow doing that he realises that it was his rival that killed his dad, and accuses him of trying to hurt Fujiko...which he did himself! In fact, this begs the question; if the ringmaster wanted to be the one and only to have access to his father's tricks, why was Fujiko the one doing the magical act? It would have brought fame to her and kept him in the shadows. If he knew that the act was flawed (and it was not, since it works), another death on stage would have tanked the show forever, so obviously it was not what he was after either.
Until Sunset, the Full Moon - S1-E7
Plot hole: Lupin tells Fujiko what happened at the Gotti Mansion while she was away, and she is surprised. The caption says it happened "2 hours ago." But turns out it was Zenigata to call the police and send them to the mansion. After that, Fujiko ran off. If she didn't know that Zenigata knew, there's no reason why she would run away. Also, you have to assume that Zenigata has been in front of the phone waiting for a long time for the HQ to call him back about the outcome of the operation, because if he *just* made the call, then Lupin's presence and Fujiko's escape become outright impossible. But it is exactly how it is shown; Zenigata makes the call, and immediately after there's Elena/Fujiko walking down the stairs.