Plot hole: The protagonist gets in the exclusive, multi-millionaire, invites-only auction because the invitation is on a printed letter that he faked. This means that the guards at the entrance don't have a guest list to check, and since nobody knows who this person is, the staff does run a background check on his identity when he makes the first outrageous bid...by looking his name up on Wikipedia. That's mighty low standards of security, especially for an auction that was supposed to be for a selected audience and the most important in France.
Plot hole: The ways Lupin enters and exits the prison don't make sense other than in a movie. He gets in timing appropriately his visit to the inmate, and performing a magic trick that requires actual magic to work; it is a trope and can be conventionally accepted as 'power' of any skilled movie thief to be able to wriggle out of handcuffs, but here he disengages from the cuffs someone else; a non-collaborating and unsuspecting individual, without having the keys and without him noticing. In a realistic series, that's a huge strain on suspension of disbelief. Even worse how he gets out; he fakes hanging himself by tying the noose to a basketball net he wears as harness. They just show him waking up in the ambulance, and that's good, because there's no way that the guards or medics didn't notice that apparatus dismounting him or attempting any first aid. They would have felt the net simply touching his shirt, even.
Other mistake: At the beginning of the episode, the date on the security camera is 29/11/2020, 1:30 am. Later when the policeman checks his phone, it's 30/11, meaning that Pellegrini waited to contact him more than a day. In episode 2, Assane's phone showed the date as Tuesday 27th Oct (timecode around 00:16:30), which would mean if true that they investigated for over a month without discussing with the commissioner the basic details, which of course is impossible. (00:02:30 - 00:13:30)
Plot hole: Fabienne Beriot is a crack investigation journalist who wrote an entire book about Pellegrini's corruption and crimes and was hellbent on dragging him through the mud. Yet she is unaware of what happened to Assane; somehow she managed to Miss in her lifelong investigation the 'small' fact that Pellegrini saved his empire by cashing in huge insurance money thanks to a very public theft that screamed insurance scam.
Plot hole: Lupin is a super-smart character who is always way ahead of his competitors. He acquires a VHS tape that is a smoking gun on his most hated enemy. He puts online (so he managed to convert it in digital format) a small clip as 'teaser' and shares it on twitter, where it goes viral. Then he goes to national TV...where the director is in cahoots with Pellegrini and plays a version of the tape that edits the incriminating part out. And that is enough to entirely defeat him. Apparently, he did not have a digital copy of the whole thing he can release to prove the editing job! It does not make any sense, especially since he knew that Pellegrini had the official media under his control, and him going on TV - lying about his own identity under a ridiculous makeup - couldn't have any positive effect worth the risk.
Continuity mistake: When Assane gives his boy a gift, look at Claire's necklace when she starts getting defensive about the 'doctor's appointment'. The chain is caught on the collar and tucked all the way up next to her shoulder in some shots and normally down in a V in the rest. (00:07:40)
Factual error: When Claire goes to the violin shop, she is told a price in French Francs, which was normal at the time of the action (1995), but when Assane talks it out with his friend at school, the currency has changed to Euros, which only came into existence in 2002 in everyday lives.