Plot hole: Waverly installs the explosive ring on Solo's finger and arms it, then says, "No one is to know you've been issued a priority ring." Odd command. It's a huge and conspicuous gold and red ring that he can't take off, and everyone at U.N.C.L.E. knows what it is. So how can Solo possibly keep it a secret?
Plot hole: U.N.C.L.E.'s yellow badges were worn only inside HQ, and were supposed to set off alarms if you didn't wear one, or if they were taken from the building. But here, Solo passes through security and walks out with his badge still on, and the alarms don't sound.