When Moe Tilden first meets the crooked cops in the New Jersey coffee shop, you can see through the window that it's raining outside, with water dripping from the eaves of the building. When he walks outside to his car, not only is it not raining but the streets are dry.
When Heflin enters his office with Tilden waiting there, Heflin's deputy is buttoning his shirt twice.
When Freddy is patrolling the fairground, Lagonda is sitting on a trash bin smoking and says "Hey, Freddy." He then disappears in subsequent shots.
The amount of dried blood around Freddy's nose bandage when at the bar talking with Figgsy and Joey changes in several shots.
Moe Tilden's mustache is noticeably longer when he comes out of the building at the end of the film. This scene took place during re-shoots, when Robert De Niro was growing his mustache longer to play Louis Gara in Jackie Brown (1997) and he didn't have time to cut it.
"Municipal" Sheriffs don't exist in the State of New Jersey. All Sheriffs in New Jersey are elected at the County Government level to a three-year term and are a Constiutional position. For a small town in New Jersey Freddy Heflin would have had to be the Police Chief or similar rank. It may also be noted that no police officers in New Jersey wear tan uniforms. That uniform is far more likely seen out in the Western states.
The unit Moe Tilden works for would never be referred to as "IA" or "IAD" by NYPD officers. It is the "Internal Affairs Bureau" and referred to as "IAB" by NYPD officers. In fact, if you read Moe Tilden's card it says "Internal Affiars Bureau."
Freddy is seen listening to Bruce Springsteen on his record player, but the gray-and-black label of the LP on the turntable is that of a Columbia "Masterworks" album of the late 1950s, an exclusively classical music label.
At Superboy's funeral, the cops are called to attention to start the ceremony but all appear to go to the position of "Parade Rest", with their hands behind their back.
In the rooftop fight scene, Joey Randone's badge number has five digits and starts with a 7. NYPD badges that have 5 digits start with either a 1,2 or 3.
When Joey Randone has fallen off the roof, his left leg is bent in an awkward angle. On the cover of next day's newspaper, the chalk line silhouette has the right leg bent. This is because the newspaper has flipped the photograph (for layout purposes). The details on the ground confirm this.
When young Freddy Heflin breaks the side window of Liz Randone's car, the window clearly breaks before contact with Freddy's head.
In one of the newspaper articles, the word "it's" is mistakenly used instead of "its" at least three times.
In the flashback sequence, when the car falls off the bridge and into the river, you can clearly see that it does not have a driveshaft or gas tank.
When Figgis enters the station during Heflin's meeting with Tilden in his office, Heflin's voice can be heard, but seen through the window of the office he clearly is not talking.
After Babitch is on the run he is visiting Heflin asking for help. When Babitch is at the door still in the shadow his mouth is clearly saying something, but we hear nothing.
In the first scene on the George Washington Bridge, he is driving from New York to New Jersey, but it was filmed going the opposite direction. Going into the city, you enter the yellow tunnel first.
When Freddy heads into NYC to meet with Tilden and IA, he walks under a PATH train sign as he walks up a stairway and then is right in the heart of City Hall and One Police Plaza, so the premise is that he took the PATH train from Hoboken to City Hall/One Police Plaza area - that isn't possible. The Path train would let him off a few blocks away at the World Trade Center area. In reality, Stallone was walking out of a subway station in City Hall with a fake PATH sign added by the director.
Freddy Heflin is supposedly deaf in his right ear, as evident from the very beginning of the film (the alarm clock scene). However at Superboy's uniform funeral, when being asked if he is completely deaf, Freddy answers that "it's just this one ear" and points at his left ear.
When Freddie shoots Ray in the bedroom, Ray pulls the trigger of his revolver as he is falling. You can clearly see the hammer cycling, but there is no shot fired.