After Supergirl ends up in the Phantom Zone (and onward), her bangs hairstyle is somehow just gone.
The judge in Lex's trial states that the trial is "The United States of America vs Lex Luthor." Almost immediately after, the head juror refers to it as "National City vs Lex Luthor."
Lex's trial bears little to no resemblance to any court proceeding that could happen under American jurisprudence.
When Lex and Lillian are playing chess near the end, Lex, playing the black side, moves first, but the game's rules traditionally dictate that the white side moves first.