Character mistake: Captain Quinn expresses not knowing what an "azimuth" is. The man is a pilot. What pilot would have never heard of an azimuth? (00:13:50)
God Is in the Details - S2-E10
Character mistake: When Diane quotes the scripture, she says "Revelations." However, it's just "Revelation." Someone as smart as her who has read the New Testament (or heard it quoted) would know the correct word.
Mine Your Own Business - S1-E4
Character mistake: When Shaggy and Scooby order Sarsaparilla at the saloon, Scooby says "Two" but he appears to be holding up three fingers.
Character mistake: Upon finding the Spanish flu virus missing, Hardison freaks out about it killing 50m people 100 years ago, saying it would be even more deadly today due to the higher population. There's no reason to think so - the death toll in 1918 was massively exacerbated by the aftermath of WWI. Not to mention today we have vaccines, plus most deaths then were actually caused by bacterial pneumonia, which today is easily treated with antibiotics.
From Agnes - With Love - S5-E20
Character mistake: Using a Texas Instruments TI-89 Titanium, the seventeenth root of 9,000,355,126,606 is 5.781163783, which means the first prime number greater is seven.
Character mistake: The doorman tells Ike that Jimmy Shoes and the prostitute left in a '55 Chevy, the car is a '56 Chevy.
The Case of the Wandering Widow - S4-E6
Character mistake: As Mr. Morgan (Dean Harens) is being examined by the prosecutor he's also sitting in the gallery.
The Dark and Bloody Ground - S1-E3
Character mistake: Clyde Russell tells Rockford to meet him at his place in "Ambazac Road in Bel Air." The name of the street in real life is Ambazac Way. (00:38:20)
Episode #1.3 - S1-E3
Character mistake: Richie Gulliver is referred to as Rory Gulliver on the newspaper headline. As he's supposedly a very well-known Member of the Scottish Parliament, it's unlikely a newspaper would make a mistake like this.
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."
Character mistake: Sasha refers to the 'murder' on Thursday 4th June 1982. The date in question was on a Friday.
Smoking Gun - S1-E2
Character mistake: When the bad guys put the generator in front of the air vent, Nigel looks at the white smoke and pointing at it says "Carbon monoxide." Carbon monoxide is colorless, white smoke is mostly condensed vapor. (00:35:20)
The Prison Prep School Murder Case File 1 - S1-E10
Character mistake: To show how hard the top students are working at the prep school, we see one of them writing; "I was at the course of a eight-week intensive." (00:04:50)
Character mistake: When Rich refers to the film showing Davis (decades ago), he figures they were in "Asia... Mongolia or somewhere." However, the film cannister had "Tibet, 1937" written on it - important enough to show the audience, but not for the character to read? (00:40:25)
Character mistake: Maxwell translates his famous line "And loving it' into the German 'Und damit gefreut'. Agent 99 who claims to speak German fluently confirms it. This translation is both far away from the meaning and doesn't make any sense at all. The right translation is 'Und liebe es'. (00:09:50)
Character mistake: In the epilogue, Charlie illustrates the relationship of mathematics to real life by discussing the golden ratio and its presence in a host of real-life situations, including the shape of a nautilus shell and the distribution of petals in a flower. These claims are disputed by some mathematicians (see http://en.wikipedia.org/wiki/Golden_ratio#Nature), and the one about the nautilus shell one is untrue (see http://en.wikipedia.org/wiki/Golden_spiral#Spirals_in_nature). It's possible Charlie is just repeating what he has read or heard without investigating it for himself, but this is uncharacteristic of him.
Character mistake: Nathan suggests to Dwight and Audrey that maybe he should shut down the meeting of troubled people. As chief, he should know he has no authority to stop citizens from assembling.
Character mistake: Javi states that his relatives have only seen Letty as a blond. But she met Ava in the hotel bar as a brunette.
The Singer - S7-E5
Character mistake: Near the end, Matlock says that he can prove who killed KC. The burden of proof lies with the prosecution; as a defense attorney, Matlock doesn't have to prove anything.
Episode #5.3 - S5-E3
Character mistake: The chief baddie spells definitely as definately.