Deliberate mistake: After the car crashes into the light pole and flips over. The top light is still functioning even though it's nowhere near the original spot.
Deliberate mistake: When the gangs meet in the toilets to set a date for the brawl, the mirror on the left is the only one opaque, most surely to avoid reflections of the filming crew.
Deliberate mistake: Denzel Washington never wears a vest (at least during the previews). All deputies are mandated to wear at least a level II vest (most will buy a higher protection vest) whenever performing Sheriff duties. Plus his duty shirt is just plain sloppy looking, way too big for him.
Deliberate mistake: After jumping off the cliff, Dom and Letty's car rolls over violently several times and finally lands on its wheels. Letty sits calmly, safe and sound, not a single scratch or bruise despite not wearing her seatbelt and having survived by just grasping the handlebar above her head.
Deliberate mistake: The Virtuoso (up several stories in a building) would not be able to hear what the boy and his mother across the street were saying. The boy even started to say "Hey, mom" when he was still exiting the building. (00:11:41)
Deliberate mistake: The view looking out the windshield showed the man on the bicycle had stopped when he was in front of the car's passenger side, but the outside view showed the man still coming to a stop and then tilting his bicycle. (00:07:12)