Character mistake: When Beth and her mother discuss the agent's fee of 15%, Beth says it is $49.54. However the prize money was $500, the expenses were $172.30, which leaves them $327.70. 15% of $327.70 equals $49.16. (00:10:00)
Remembrance - S1-E1
Character mistake: Picard and Data are playing poker at the beginning of the episode. Before the actual faces of the players are revealed, we are shown close-ups of their hands as they put down the chips for the bet. When Picard says his first line in the series it's "See", and it is literally true, because in the previous shot, Data put his 5 cards down on the table and face up. (00:00:50)
Character mistake: The FBI team responds to a murder crime scene. The victim is lying face down in the bed with blood everywhere. The team leader takes the victim's wrist with his bare ungloved hand. A trained FBI agent would never touch a murder victim without gloves - one to protect himself and two not to contaminate the crime scene. (00:10:00)
On a Wing and a Prayer - S4-E7
Character mistake: FO Woodham drops James in Darrowby. James gives a proper RAF salute (palm forward). Woodham responds with a US style salute (palm down).
Angel of Mercy: Part Two - S1-E4
Character mistake: When Lenore Osgood is speaking on the phone with Charles Wainwright about killing Dr. Hanover, she mispronounces "Larynx" as "Lar-nix."