At the hospital, Fran Sr. and Ray are in a restroom. Fran washes his hands and struggles a bit to reach in and pull a paper towel from the dispenser. Four or five times the camera cuts back from Ray to Fran and the dispenser alternately has the towels hanging out, then tucked in, then hanging out again.
Where Raymond and Francis, Sr. are in the bathroom, Francis urges Raymond to join the Task Force. Francis removes towels from the dispenser. In the next two subsequent shots, the position of the towels at the dispenser has changed.
When Francis arrives at the initial crime scene, he tells Billy to hang on as the ambulance is wheeling him out. Billy has a non-re-breather mask on, but no oxygen is being administered because the bag on the mask is deflated.
In the scene where Ray is staking out the junkie informant in the Santa hat to find Tezo, when he he jumps out of the car and starts running, he has an empty, unsnapped and flapping holster on his left hip (rear view) but is not carrying a weapon in his hand. When we next see him, he has the holster on his right hip, gun in it and snapped closed. He then un-holsters his weapon from that left hip holster when he readies to enter the building.
When Ray and Franny are driving to the convenience store, you can see the reflection of the same Duane Reade drug store over and over again in the car window. It is a continuous loop.
When Colin Farrell threatens to burn the baby, he says it has severe "1st degree burns", but he means "3rd degree burns". A plausible explanation is that in Law Enforcement, the lower the number on the charge means the most severe, (1st degree theft more severe than 3rd). It's the opposite for burn terminology.
When the car is set on fire, the blaze is clearly started from underneath the car, not inside it where the gas was poured.
During a few scenes towards the end, Ray flashes a badge and states "Detective..." The badge he is holding is in fact a NYPD Captain's badge (shield) and not a Detective badge (shield).
In the bar prior to the fight, Ray displayed either a captain or deputy inspector's shield, since he's portraying a detective, not sure how he got promoted so quickly.
In the bar scene, the camera is on a man playing pool who is about to make a shoot but he is hitting a striped orange ball instead of the cue ball.
As Jimmy and Ray are preparing to fight in the bar, each places his badge and gun on the bar. Jimmys gun is still in its holster and we can see that his holster is one that threads through belt loops. Meaning for him to have removed the holster he would have had to take his belt, at least part way off.