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.
The Wedding - S8-E23
Character mistake: When Roseanne, Darlene, Jackie, Bev, Becky, and Nana Mary are dressing for Darlene's wedding, Nana Mary comments that all of them were pregnant when they married. However, Becky, was not pregnant when she and Mark eloped and they never had children together. Roseanne was not pregnant before marrying Dan. When the series began, Becky was 13 years old and Dan and Roseanne had been married 15 years.
Character mistake: When discussing Ensor, Avon says he'd spent 20 years of his life in hiding. Yet in 1-13 "Orac" Blake said he hadn't been seen for 40 years.
Character mistake: Sasha refers to the 'murder' on Thursday 4th June 1982. The date in question was on a Friday.
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: When Collier is meeting all the 4400s at the reunion, Shawn calls Isabelle Maia by mistake. (00:31:10)
The Devil Made Me Do It - S1-E8
Character mistake: In his discussion with Joan about the belief that the devil sometimes disguises himself as God, Father Ken calls the Book of Revelation "Revelations."
Character mistake: Nick asks Janette if she's ever turned anyone else into a vampire - an odd question, considering the fact that he already knows she has. He was there when she brought the baroness across in the 18th Century flashback sequence for "If Looks Could Kill." It's even odder that Janette tells him she's never done it, since she knows that Nick knows she has. Apparently, the only one not in the know here was the scriptwriter.
Dedication - S1-E7
Character mistake: When they show the helicopter containing Alpha team, it is a Bell 206 JetRanger, and the sound effects match it, but Brown says "This is the first time I'm on a Huey." The Huey and JetRanger look and sound nothing alike. (03:25:00)
Character mistake: Sue White suggests speaking in Portuguese but what she says next is actually Spanish. (The subtitles incorrectly say she is speaking Portuguese). (00:04:00)
The Night of Miguelito's Revenge - S4-E12
Character mistake: The store window's sign says, "Denver Mercatile" rather than "Mercantile."
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.
Character mistake: Edith says in a story that Archie has a brother Phil. In actuality Archie had 1 brother, Fred.
Character mistake: When Betty and Daniel takes Oshie to the White Tassel, as they are walking in, Daniel asks Betty if she is sure that they do not have anything over $5, Betty smiles and agrees. However, when there is an establishing shot of the restaurant, it states in the window that there is something for $9.99.
Children of Earth: Day One - S3-E1
Character mistake: Lois says that Colonel Aduya's uniform "isn't British Army". In fact, it is entirely (and accurately) British Army with the exception of the small UNIT badge over the pocket.
First Blood - S12-E9
Character mistake: Sam points out Elk Mountain, but there is no Elk Mountain in Rocky Mountain National Park.
Character mistake: Dr. Sloan and Quinn are in the victim's apartment. Right before Dr. Sloan opens the door for the old lady witness to ID Quinn, Dr. Sloan says, "saw a man visiting Holly the night before he died." Holly is a woman. Dr. Sloan should have said "she." (00:33:51)
Character mistake: In one episode, John, Meldrick and Tim are called down to their bank because they're getting a business loan to buy the Waterfront Bar (the bank's policy is to give good news in person). They start arguing and Tim announces at one point that "I've got a platinum card, Frank", which is marvelous, except he's talking to Meldrick.
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.
Character mistake: When Walker and Satch are in the car looking for Walker's son, Walker tells Satch his son is 17. Afterward, when they are out on the streets, Walker asks some people if they have seen his 18-year old son.