Continuity mistake: Right at the beginning of the episode a Cadillac Escalade gets stolen. The car is the newest model. The chase begins and the car is a new model right up to a scene when they crash into some other cars. That part was filmed with older model Cadillac. The damage is quite severe, but the chase continues again with the new model that has only one bit of damage - a mirror that has come apart.
Factual error: In Oregon and New Jersey, state law requires that a gas station attendant pump the gas. Romero pulls into an Oregon gas station and encounters a nosey person. They are both pumping their own gas.
Factual error: Sierra Nevada beer would not have been available in DC during this time period.
Character mistake: When Olivia and Dr Galina are in the bathroom, Galina mentions an umbilical chord, from a baby whose mother died (Nadia), that contained Olivia's mitochondrial DNA. Mitochondrial DNA comes from the mother, so Nadia's Mitochondrial DNA came from Letha who got hers from Marie, absolutely nothing to do with Olivia.
The Sins of the Father - S4-E9
Factual error: A character is revealed as having been hypnotised into committing murder against their will. This is not possible. (00:05:20)
Episode #1.4 - S1-E4
Revealing mistake: The tabloid story with the plight of the Latimers just came out, and various characters are looking at it. In the bit when David Tennant tosses on the desk his copy of the Herald, the second paragraph of the second column goes "Sitting in the family home, surrounded by pictures and mementos of Danny" etc. It is the same text that was at the very beginning of the article when the store owner was looking at it. The newspaper is a prop with the same text in a loop. (00:35:00 - 00:36:30)
Factual error: The FBI agent introduces himself and says "Mike Weston - I did my thesis on Joe Carol at the academy." FBI agents are required to have a university degree, but they don't write thesis' at the academy. A person is either in a university or at Quantico getting trained. They are not writing papers at Quantico. They need the degree beforehand to get in. (00:10:30 - 00:11:30)