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.
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)
Continuity mistake: Front and side views of the bouquet of flowers do not match. Most obvious is the large orange day lily that sticks out at the top on side views. The flowers also look different (more orange ones) when they are being brought into the patient's room. (00:02:21 - 00:02:53)
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)
Continuity mistake: The second time Randy's nude body was shown lying face down on the bed after Alex killed him, his buttocks were arched/curved more and higher (not as flat). (01:07:21)
