Other mistake: When Agent Wells tells the White House they need to alert the Pentagon that Lozano is inside the Pentagon, she is told "it's already done, they are locking down the building right now." Then, later in the same episode, we see Lozano use a key card to easily pass through the building. (00:15:45 - 00:21:15)
Other mistake: In the beginning when Kali and her gang are running from the police in Pittsburgh and she "collapses" the tunnel, her 008 tattoo is shown this way so we can read it as such, but it should in fact be read 800 to be the correct way. (00:03:15)
Other mistake: Archie's uncle Frank tells Archie during an argument with him that he is 40 years old, with seven years in combat while in the military. But in a previous episode when explaining why he let Fred take the blame for his DUI, he claimed that he was a Desert Storm veteran in between tours at the time. Either the show got the wars wrong and meant to say he was an Operation Enduring Freedom or Iraqi Freedom veteran (no actual veteran uses "Desert Storm" when referring to combat in the Middle East after 9/11) or they're saying that he was only 10-11 years old when he went to Desert Storm. (00:29:30)
Other mistake: A major plot point is the rivalry between the Wehrmacht and the SS, who refuse to work together. After the explosion at the cemetery, it is the Wehrmacht who are explicitly described as rounding up and interning suspected resistance fighters, with the SS not being party to it. However, when Archer visits the internment camp, most of the staff are wearing SS uniform.
Other mistake: In this true crime show there are both reenactments and actual police photos used. The narrator states that thousands of rounds of ammunition were found in the home where a crime was committed. But the accompanying "Actual police evidence" photo that's supposed to be ammo is actually stacks of Kodak Slide Carousels. (My dad was a photographer and we had these in my house.) (00:29:15)