When Lupin is clutching his throat, he drops his glass and it's heard smashing. Over two minutes later, when he's asleep, the glass is near his hand and had merely toppled over. Then when Dr. Normil and Lupin's impostor enter, the glass is gone.
In the first shot of Lupin passed out over the table, his jacket is fully on. Then when the scene cuts away from him and then back to him, his jacket has partially slipped off of his right shoulder.
Lupin only set up one camera in his hotel room, yet the footage showed the scene from multiple angles.
There's no explanation as to how Jigen and Goemon didn't hear Lupin falling over and hitting the table. Furthermore, there's a chance Lupin would snore or groan or use the last of his strength to say something, which means Dr. Normil would have had to do a timed soundproofing of the room, which he somehow managed to do without Lupin's partners noticing.
Several news items show the Fake Lupin committing crimes and generally being cruel in broad daylight, which should have caused Lupin and his gang to see through the whole ruse, given that they've been told that Lupin only changes at midnight.