Factual error: The movie starts in 1985, jumps '5 years later' and then back to Sasha Luss, then '3 years earlier'. So, in her crusty apartment in an impoverished neighbourhood of 1987 Soviet Russia, Anna is filling a form on her notebook-style laptop, too modern for the era. It looks like a NEC UltraLite (considered the first notebook style laptop) which didn't even come out until 1989, let alone the likelihood of someone in the USSR having one.
Factual error: The movie starts in 1985. In the first arresting scene, one of the American spies is using a flip mobile phone.
Factual error: This film takes place in the late 1980's and then 1990. A normal hard drive was capable of storing 40MB, the more expensive and advanced ones could store 100MB. Anna kills her target and some guards and goes to the security office to remove the hard drive with the recordings for all the cameras. The technology wasn't there for that entire scene in 1990. She would've needed a few wheelbarrows for the amount of hard drives needed to store that amount of data. (00:52:00 - 00:53:00)
Factual error: When the old woman drops her off at her new flat, we are treated to the delicacy of a balcony view from which we can see modern Suzuki cars.
Continuity mistake: When Sasha is jumping from the stairs at the end, she is wearing black tights, but before and after she is wearing different tights.