(at around 46 mins) When Zukhov is speaking with Elizabeth at his home, the last scene before it cuts to commercial, his ribbon bar on his uniform has become unclasped and his ribbons are hanging down.
Zhukov's shoulder straps are not only sewn along the entire length (which is why actor Olek Krupa can barely move his shoulders in the scene) but they are also sewn inside out. The stars should be on the outside of the strap. The collar insignia are also turned upside down.
Colonel Zhukov's shoulder marks are attached the wrong way - the stars must be close to the arm and not to the neck.
In one of the first scenes, an establishing shot of Moscow is shown. Prominently featured is the Cathedral of Christ the Savior, which was demolished by the Bolsheviks in 1931, but rebuilt to exact specifications in 2000. At the time this series takes place, in the 1980s, there would have been a swimming pool there, not a church.
In a scene that was supposed to take place in the Soviet Union, an American-style three prong outlet is clearly visible in the background.
When Elizabeth leaves the agent on a bench outside of a park, the flag of the State of New York is clearly visible, despite the fact that the scene was meant to take place in Washington D.C.
In the Flashback where Elizabeth is supposedly walking with Zhukov in Rome they walk in front of a flat faced building towards a square containing a metal sculpture under a gray sky. A skyscraper can be seen in the background. This is all very much unlike Rome. The scene was filmed at the Magnolia Plaza and Central Pavilion at The Brooklyn Botanic Garden, NY.