Continuity mistake: In the scene where William Fichtner is shown first leaving his trailer and picking up litter in the amusement park, his gloved hand switches from his right hand to his left then back to his right again before he starts talking to the couple. (00:05:40)
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.
Character mistake: When Gina tries to set up Rosa on a date, Rosa mentions the last person Gina set her up with (Justin) was a dork who rode a Yamaha motorcycle. She says "he might as well have picked me up in a station wagon." Rosa's bike is a Yamaha R1.
Factual error: Sierra Nevada beer would not have been available in DC during this time period.
The Governor's Pleasure - S3-E1
Plot hole: The governor refuses to open the door for the prisoners when they have Vera hostage, and you can hear her saying "no" "return to your units" over the radio, which Channing had to overrule. Later on in the show somehow Vera doesn't know the governor refused and has to find out from Channing. But Vera was there next to the radio the whole time. They use normal radios without earpieces so there is no way she didn't hear. (00:38:05)
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)
Continuity mistake: Bunchy is serving burgers. Picks up ketchup in his left hand and mustard in the right. Camera pans from a different angle and he is putting back the mustard and picking up the ketchup that he already had. (00:28:11)
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)
Factual error: In the scene where Bonnie gives Clyde the unloaded pistol through the jail bars, that gun was not manufactured until after 1972. It is a Bauer .25 ACP semi-automatic stainless steel pistol. Bonnie and Clyde's reign of lawlessness ranged from 1931 to 1934.