Plot hole: Mr. Varner spots Illya down the street and says, "I think he's another U.N.C.L.E. agent." His uncertainty is odd: he helped identify and chase Illya earlier in the episode, so he already knew to be fact what he only "thinks" in this later scene.
Factual error: Mandy reveals at the end that she's been carrying the microdot hidden inside her contact lens. Ouch. Any foreign object placed inside a contact, especially the hard glass contacts of the 60s, would cause irritation severe enough to make the lens unwearable and the eye very, very red.