Character mistake: After Vincent and the other FBI agents entered the room where Alex had tended to his wound and left bloody tissues and other evidence on the table, he and Maryanne sat at the table and handled evidence (e.g, firing pin) without wearing protective gloves or preserving evidence in protective bags. The room (and bakery) had not been secured/ roped off, but a few agents walked around, potentially disturbing/destroying evidence. (01:19:09 - 01:24:05)
Character mistake: Danny told Vincent, "Lab just came back on the pills. Donepezil. Alzheimer's drug. Your shooter's losing his shit." It was too early in the investigation to conclude that the drug belonged to "the shooter." There could have been a witness who ran, an accomplice, or even just a coincidence that someone not involved had dropped his pills. It would be up to the investigators to determine if the prescription bottle belonged to a suspect or "person of interest." (00:55:27)
Character mistake: The SWAT team member could not see the faces/bodies of the two people under the sheet exiting the hospital, but identified Dr. Meyers as the one on the left. SWAT then asked, "Sniper two, do you have a shot on the subject on the right?" The sniper killed Dr. Meyers (a hostage) instead of intended target Alex. SWAT would/should not order a sniper to shoot at someone who could not be seen (positively identified). (01:38:18)