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)
Bank Run at Mr. Bank's Bank - S13-E6
Character mistake: When Archer and Ray are being shown the security controls by the bank employee, there is a corkboard on the wall behind them. On the corkboard, there is a paper with the caption with the "Missing - My Favotire Mug." Clearly it is meant to say "favorite", but the R and T were misplaced, resulting in a typo. (00:11:40)
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)
Continuity mistake: In episode 6 - Once Bitten, Krieger is using the system, but has no training to do so. After Mallory berates him, Krieger states: "Yeah, I don't actually know how any of this works - that was the fat guy you killed". But the "fat guy" who does the satellite monitoring stuff doesn't die until this episode - a shock induced heart-attack after receiving a hard slap from Mallory.
Suggested correction: The episodes were aired out of order than what they were produced. "Coyote Lovely" was the 2nd episode of season 4 to be produced. So, as it was written, the fat guy dies before the events of "Once Bitten."
Other mistake: At the start of the scene where Mallory says she is going to the premiere with Burt Reynolds, there is an establishing shot of the building. Just over a minute later, the same shot is repeated a second time, as shown by the fact that the cars driving by the building and the cars parked in front of the building are exactly the same. (00:06:30 - 00:08:00)