Episode #2.3 - S2-E3
Character mistake: DS Maxwell comes to Katy's house to interview her but when he introduces himself he says "DI" Maxwell.
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.
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.
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."
Episode #1.2 - S1-E2
Character mistake: In the incident room Danny's height is written as 4ft 8inches / 112 cm. 4'8" is 142cm. (00:06:48)
Episode #6.4 - S6-E4
Character mistake: The character pretending to be Lt. Ellis refers to himself as First Lieutenant. That rank is referred to orally as "Lieutenant", not "First Lieutenant."
Looking for Mr. Goodbrain, Part 2 - S3-E13
Character mistake: When Liv and Clive are talking to Chase about Katty, Liv tells Chase he had a cocktail napkin with Katty's phone number on it. However, it was only Katty's hotel room number that was on the napkin, which Liv saw.
Compromised - S1-E9
Character mistake: When she and OA meet Marshal Ackerman, Maggie is somewhat surprised to learn Damon Cruz was a federal witness. As a federal agent herself, Maggie surely would know that the Marshals Service's mandate includes the witness protection program.
One Good Man - S3-E6
Character mistake: After Patton's ex-wife pushes him off the balcony and he lands on the researcher with the gun and the rest of the team come in, someone asks him if he is OK. He says that he is fine, nothing is broken. Other than his arms, ribs or neck how is he going to know that? He is already paralyzed. He can't feel anything.
Character mistake: Lorraine mistakenly tells Denny to "call 999" instead of 911, and when asked about it by Katie, denies having ever spent time in the UK (later revealed to be a lie). But this isn't some high-pressure slip of the tongue, she's highly intelligent and has been in America for a decent length of time, is working hard to maintain her facade of being born and bred American, so there's no way she'd slip up over such an obvious thing.
Episode #3.4 - S3-E4
Character mistake: DS Miles while in the chocolate shop tells Ana to go with "DCI Riley." Riley has the rank of DC, not DCI.
Character mistake: When the sergeant's partner gets shot and Chen calls it in, she says he got away in a black Buick, but the car was a Honda Civic. (00:10:52)
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: The X-ray shown when Ruth see Cade's body is placed in the wrong way. It should have been a mirror image. (00:57:56 - 00:59:06)
Flashpoint - S1-E5
Character mistake: Chief Pope threatens to take away Lt Flynn's stripes. Lieutenants don't have stripes.