Revealing mistake: While the ODIN agents are hallucinating, one can be seen looking into the barrel end of an MP40. If you follow him as the scene continues, the gun clips out of the sprite's visible area, and is almost entirely gone. (00:14:30)
Continuity mistake: In "A Going Concern", Archer has the microchip implant removed that Nikolai had put in in "Dial M for Mother." When they put it in, they drilled a hole on Archer's left side and put the microchip in there. But now, the band-aid shows they removed the microchip from Archer's right side.
Other mistake: Archer, Lana, and Ray are discussing their plan to rob the casino. When the scene plays where Lana and Archer take out Lachouffe's guards, Archer cocks a pistol that is pointed at him in the wrong direction, which would be physically impossible. (00:12:55)