(at around 37 mins) When the coroner holds his hand out to shake Maya's hand, there is blood on his gloves. When he takes them off a moment later, there is no blood.
(at around 34 mins) During the car chase, all exterior shots of the car clearly show that there is no passenger even though Maya is shown from the interior to be sitting there.
(at around 34 mins) The mud disappears and reappears very obviously in the car chase scene multiple times.
(at around 34 mins) During the chase scene the relative position between the two cars keeps jumping in impossible ways.
For safety purposes, all handcuff keys are standard. In case of emergency, if some handcuffs need to come off immediately, it wouldn't be advantageous to need to find the right key, so for that reason, every handcuff key is the right key for every pair of handcuffs. When the agent handcuffed the sheriff, the sheriff didn't check his pockets for a key, and the agent seemed confident that the sheriff was securely trapped. The scene suggests that handcuffs are like padlocks, and only the agent's key can unlock the agent's handcuffs, and that's not how handcuffs work.
(at around 16 mins) The killer is supposed to have been an EMT however when he performs CPR on Penelope he doesn't tilt her head back enough to ensure a clear airway for mouth to mouth and when he is doing chest compressions his hand are placed on her abdominal region not her chest. These are mistakes someone with formal EMT training would not make.
The sheriff's department jackets have the reversed US flag on the front of their jackets. This is normally worn as a shoulder patch.
(at around 36 mins) In the morgue you can see the woman who is dead on the table breathing.
(at around 1h 22 mins) In the end scene with the credits where you are seeing scenery you can clearly see towards the top of the screen the helicopter blades used to shoot the scenes.
(at around 1h 22 mins) During the closing credits, the helicopter from which the aerial shots are filmed is visible in several shots, usually as a shadow on the ground. In a few shots the flicker of the main rotor can be seen at the top of the screen.
(at around 25 mins) When Duncan is taking Maya's pulse, he uses his thumb to check the pulse which is incorrect, as it has its own pulse.