Zhukov has his epaulets upside down (he is a colonel-general, general polkovnik)
The airline ticket that Irina gave to Philip was modern laser-printed boarding pass with tear-away tab. The tickets issued in 1981 would have red font colour (from red carbon coatings underneath each sheet), and they are either handwritten or typewritten.
When Philip is walking away in NY after mugging the woman he approaches a Verizon telephone truck - Verizon didn't exist in this period. It would have been either Bell Telephone or NYNEX, depending on the year of the show.
The Amtrak train that Phillip rides to New York has paint schemes on the engine and cars that were not correct for the time.
The German passport we see in the interrogation scene is red, but at the time the series is set (1981) German passports were green. The inner part of the passports with the photo is also not correct, regarding the photo and writing.
Characters says "We all have our issues." The incorrect substitution of issue for problem in speech did not begin until the 21st century.
When Irina is asked if she speaks Polish, she says the equivalent of "Yes, a little," but only the word for "yes" ("tak") is in Polish, and the rest is said in Russian.
At 14:07 when Philip "helps" Jerry to his seat, Matthew Rhys very briefly looks directly into the camera.