Continuity mistake: When the FBI realises that the Ford Bronco that Alex Lewis shot an El Paso PD officer from was full of pigeon droppings, and Det Marquez remarks that Lewis' burned-down family bakery was full of pigeons, it can be seen through the office windows that it's still daytime outside. However, when the FBI arrive at the bakery, it's late at night. It is unlikely that the FBI would take hours to show up at the bakery given how time-sensitive it was to find Lewis, or collect evidence on his whereabouts.
Factual error: El Paso, Texas, where the entire movie is set, is nowhere near the ocean or large enough bodies of water where a marina with moorings for megayachts could be located. The yacht scene, while fanciful, could not have taken place in El Paso or anywhere reasonably nearby (even by US standards).
Other mistake: Alex's prescription bottle on the table appeared to have 4, possibly 5, pills in it. When he heard the FBI agents coming into the bakery, he held the bottle up to his mouth and took an unknown quantity (apparently, more than one) then threw the bottle on the floor. Vincent brought the prescription bottle to Alex in the hospital. It could not be seen how many Alex took (again, apparently more than one). The rattling sound afterwards suggested there were still several pills in the bottle. (01:16:58 - 01:27:41)
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)
Other mistake: A bottle of prescription pills dropped onto a cement parking garage floor is not likely to have its cap come off (unless it was already loose). If the cap does come off, the pills (especially round ones) are not likely to settle around the bottle, but the police photo showed the pills clustered around and in close proximity to the bottle. Also, Alex - a professional assassin - did not bother to at least pick up the prescription bottle that had his name and other identifying information on it. (00:44:30 - 00:48:30)
Revealing mistake: In the scene wherein Detective Marquez and Senora Borden are drinking wine by the (indoor) pool, the back of Det. Marquez's head is disproportionately large. Front views of Det. Marquez often show his head tilted to the left, but rear views usually do not and his head might even be tilted to the right. Also, Senora Borden's eyes do not appear to be aimed correctly at Det. Marquez's (especially since they are facing each other with heads tilted to the right). Use of stand-in and/or green screen. (01:02:30 - 01:03:10)
Continuity mistake: At the FBI office, Vincent's body position while standing next to (or partly behind) the chair changes a few times within about 20 seconds, from most to half to all of his lower body visible. The position of his right arm also changes, from resting it near the edge of the chair's back or closer to the middle. When the camera returns to him, he is usually standing still, not moving or fidgety. (00:26:52)
Factual error: FBI agent Vincent brought Alex's Alzheimer's prescription to him in the hospital and Alex immediately took at least one. Only the attending doctor, nurse, or other authorized hospital staff member should dispense a drug (prescription or over-the-counter) to a hospital patient. (01:27:40)
Continuity mistake: After Alex attended to his wound, he was sleeping with his left arm straight across the table and his left hand between a lantern and bottle of alcohol/whiskey. A distant view of him getting up shows the lantern at a different angle and much closer to the bottle of alcohol. The part of the laptop that was under his hand was moved back. When Alex sat back down at the table, the lantern was closer to where it initially was. (01:16:22)
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)
Deliberate mistake: The large round blood spot Alex left on the side of the building was where his right hand would have been (or made to appear) and did not seem possible. Later, it was revealed that Alex had been shot below his stomach on the left side, seemingly explaining the large blood spot on the building - except Alex did not have that part of his body close enough to that area of the building. (01:10:07)
Deliberate mistake: Due to some unknown factors (e.g, time of night), the doves' or pigeons' behavior in the boarded-up building falls short of "factual errors." Doves respond to sound and movement, so would have flown to higher spots when Alex was at the door. Doves typically roost up high, so it is questionable why they were at floor-level. If/when doves do sleep on/near the ground, they do so in a lighter mode (one eye open) and, when spooked, would have flown away at roughly the same time, not at intervals. (00:51:15)
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)