The seal behind the judge implies that the trial is in federal court. If it were in federal court, the prosecution would not be done by the District Attorney but by the United States Attorney.
The seal behind the judge in the courtroom depicts the "United States District Court for the District of New York City." There is no such court, the correct district in Manhattan would be the "Southern District of New York."
The box car full of dirt does not have a roof opening or chute, so there's no way the car could be filled with dirt.
The flag on the back wall of the court room does indeed have 48 stars. However, there is another flag on a stand near the judge's bench., which is the correct placement for a US flag in a US court. This second flag hangs limply, so there is no way to know how many stars are on it. The flag with the 48 stars is likely just set decoration.
During the fight scene at 23 minutes, the movement of Daredevil going up the pallets of rice and Elektra going are unnatural, revealing the wire work during this scene.
Foggy fails to object to two aspects of Castle's trial. First, Castle is brought into the courtroom in a prison jumpsuit. Secondly, D.A. Reyes says that Castle killed 30 people "that we know of." Both of these could be seen as prejudicial to the jury. The second, in particular, accuses him of crimes for which he is not actually on trial.
Foggy mentions to Karen about the judge calling the first witness. Judges don't call witnesses, the prosecution and defense call the witnesses. As an attorney, Foggy would know this.
When discussing their legal strategy, after Matt proposes beginning with PTSD, Karen says, "so you think the war is made what Frank what he is." She likely meant to say "the war is what made Frank what he is" but transposed some words.