Character mistake: When Aiden and Melinda go the the hospital to visit Jim/Sam the picture on the hospital badge is of Jim Clancy not Sam Lucas... Jim has been in Sam's body for many years at this point. You can see the badge multiple times in the episode.
What Happens at Home... - S6-E10
Character mistake: After the murder that takes place while the team is at the church meeting, they gather together to talk about narrowing down the suspect list to the people who didn't show up to the meeting. Spencer shows up with a stack of papers and says 18 suspects didn't show up. We then see his actor break character and almost laughs when he looks over at Ashley, whose actress too almost breaks character from laughing.
Character mistake: Meredith admits during the ethics seminar that she has been sleeping with Bruce, the HammerMill rep, for discounts on paper/paper supplies for the company, as well as Outback steak coupons, for 6 years. But, Dunder Mifflin did not begin selling Hammer Mill products until 3-2 "The Convention" when Michael got the contract.
Character mistake: When talking to a family, Christina says that the patient had "hematomachrosis" instead of "hemachromatosis"
Character mistake: While looking at a doctored photo of Lincoln and his mother, Lincoln mentions that Michael was born in 1976, but at the end of "Killing Your Number", it reads on Michael's grave stone that he was born in 1974.
The Man in the Fallout Shelter - S1-E9
Character mistake: Hodgins is talking to Bones and says something about Goodman not being able to see his family and Zach not being able to see his kids. Goodman has kids, Zach was going to visit his family, not the other way around.
Suggested correction: With Zack's kids, Hodgins was referring to the 40 cousins and nephews that Zack has, and sees every Christmas.
Character mistake: When Rose thinks Mickey is dead, she says she'll have to tell his mother. But in Rise of the Cybermen in Series 2, she says that Mickey's mother has been dead since he was a child. (00:30:17)
Character mistake: Patterson - the oceanographer - at one point claims that Lithuania is land-locked. She should know better; in fact, Lithuania has a coastline of close to 100 km on the Baltic Sea.
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: 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)
First Blood - S12-E9
Character mistake: Sam points out Elk Mountain, but there is no Elk Mountain in Rocky Mountain National Park.
Flashpoint - S1-E5
Character mistake: Chief Pope threatens to take away Lt Flynn's stripes. Lieutenants don't have stripes.
Suggested correction: Michael didn't establish the contract with Hammer-mill. Rather, he locked them up as an exclusive supplier. It's unknown if they were already selling the products to Dunder Mifflin alongside Staples and Office Max.
Wrong, Josh says they cannot sell Hammer-mill products as they are exclusive to Staples so therefore they wouldn't have been able to sell there products alongside as mentioned before until Michael made them an exclusive to them solely, Dunder Mifflin. Therefore the original mistake stands true.