Stupidity: The team can hack security cameras and gain access to Pam's laptop easily and load the image they want on her screen, but then have to email it to themselves for some reason rather than just transfer the file directly via the connection they already have to her machine. Ridiculously insecure and an unnecessary step.
Suggested correction: You're not wrong, but that segment is far more flawed. In reality, hackers never use the "remote desktop" technique, which has high bandwidth overhead and would require constant distraction of Pam to prevent her from noticing the blatant intrusion on her screen. Real-world hackers typically open a file-sharing connection to analyze the victim's PC, avoiding any interaction with the screen, mouse, keyboard, or email address.
Stupidity: Stephanie googles (using the actual Google engine) the name of Emily's fiancé but gets zero results. He is the heir of a mob family embroiled in decades-long feuds, a central figure in the Roman nightlife travelling with private jets, with the newspapers having covered their earlier relationship. Therefore, the chances that absolutely nothing exists online are exactly zero. (00:19:05)
Stupidity: It took Leroy and Charlie too long (16 seconds) to realise the real J. Daniel Atlas is in their apartment, and he's not a hologram. It would take a microsecond for an ordinary human. (We, the viewers, knew immediately.) (00:10:48)