Visible crew/equipment: As Joe approaches the third car with the bad guy in it, there is an unknown man, possibly a crew member, reflected in the back window where there wasn't a man before.
The Hit-and-Run Driver - S1-E12
Visible crew/equipment: In the street scene, after Friday and Gannon have crossed the street, a blue station wagon passes in front of the camera. The lights, crew, and camera are reflected on the car's panels.
The Bullet - S1-E17
Other mistake: After learning Carl Hamlin had been shot with a 9mm bullet instead of a .38 revolver, the detectives, along with Ray Murray from SID, return to the scene where they conclude no one could have shot Hamlin and left the study. Murray asked Friday if they had seen an empty shell casing, to which Friday correctly replies that "there was no reason to look for one." However, they start to look around the study to find one after already realizing that he could not possibly have been shot there.
The Big Dog - S2-E11
Continuity mistake: As Joe and Bill take off to pursue the fleeing station wagon, Joe is talking to the mic in his right hand. When the camera cuts in for a close-up, it's in his left hand.
Character mistake: The second Mrs. Loomis describes Mr. Loomis as having brown eyes to Friday and Gannon. Later when they are interrogating Loomis, a close-up on his face show his eyes are blue.