Marsha, Queen of Diamonds (1) - S2-E23
Continuity mistake: After Batman has been hit by Marsha's love dart, when Robin pulls the dart out and then begs Batman to resist it, in these semi closeups note Burt Ward's uncovered forearm with his still-healing burn wound. Then, while the Dynamic Duo fight Marsha's sabre wielding goons, Marsha hits Robin with another one of her darts and orders him to attack Batman. When this happens, Burt Ward's forearm now has a compression bandage around the wound. (00:13:55)
Continuity mistake: The lighthouse keeper's pistol keeps changing distance from Sgt. Troy's head between shots.
Continuity mistake: After prying off the lock to the storeroom with the pry bar, Doug drops it on the ground, but the next shot of him entering the storeroom shows it still in his hand.
The System - S3-E15
Continuity mistake: Phelps takes the tape from the recorder's right-hand spindle. When he opens the acid vat, we can see the tape he just removed back on the recorder - but on the left spindle. The tape he then drops into the acid doesn't remotely resemble the one he pulled, and when he drops it, the recorder's left spindle, where the full tape was in the last shot and where the empty reel should be, now has nothing on it at all. (00:02:50)
Crime Wave - S1-E4
Continuity mistake: Kato activates the clamps that prepare Reid's car for the flip-over that will reveal the Green Hornet's "Black Beauty." We see the clamps hook themselves to the car in close-up. But in the next, wider shot of the car turning over, the clamps have disappeared. (00:05:00)
The Moulin Ruse Affair - S1-E17
Continuity mistake: From the outside, the U.N.C.L.E. building's wall is made of red brick. But, after a large hole is knocked through it, a shot from the inside shows no red brick at all. In fact, the entire wall is now made of white cinder-block. (00:02:30)
The Sleeper Shall Awake/Where Walks the Sleeper/The Final Sleep - S1-E11
Continuity mistake: Part 3: As you see the third "Sleeper" (a giant bomb shaped like the Red Skull's head) note the position of the monocle. First it's on its right side, then its left side, and back again to its right side. (00:14:20 - 00:15:05)