Plot hole: All those years in the spy biz as U.N.C.L.E.'s very famous top agents, and Solo and Illya are still able to successfully go undercover with little or no disguise. Here, all Illya needs is a phony mustache and an even phonier accent. And of course (gotta love it), the Thrush bad guys still don't recognize him.
Revealing mistake: There are several dead giveaways that the New York City street Solo and Illya walk down is actually in Los Angeles. They pass Mexican taco/burrito stands and shops with "Happy Holidays" painted on the windows, yet it's warm and sunny and the passersby are in shirt sleeves. The windows also reflect a number of towering California palm trees.