Renko's very obvious black eye almost completely disappears in a matter of several minutes.
In the first morgue scene, the wide shot when all three bodies are visible, the tables with the instruments are covering their shins. In the close up shots the tables are covering their thighs.
When Arkady stands up to leave the hotel bar, the bowl of peanuts is sitting on the arm of his chair, but after he leaves, Kirwill reaches down for the bowl as if it were sitting on the floor.
During the final scene, pine martens were substituted for sables, clearly identifiable by the yellow fur on their chests.
When Arkady's car stalls on the bridge on the way back to Moscow, the wipers are still running. As Arkady repeatedly tries to re-start the car, the wipers are still running at full speed. In real life, each time he tried to restart the car, the wipers would slow from the current drain of battery power from the wipers to the starter motor.
When Arkady chambers a .32 ACP cartridge in the assassination pistol the cartridge's primer has already been spent, as evidenced by the deep impression in the center of the head (base) of the cartridge.
Phone booths in Soviet Union 1980s were painted yellow and red.
When the two are shot on the stairs, the suppressor on the gun is not inline with the barrel of the semi-automatic pistol - it appears to be bent downwards a bit. So, when fired, the suppressor would have been blown apart. A poor job done by the prop department or armorer.
The lousy dubbing of the friction noises made by the skate blades on the ice.
The pistol and suppressor used in the stairwell murder scene are significantly misaligned, which is easy to see when the killer descends the staircase.
At the cottage, a woman (Natasha) approaches Renko and his friend and offers them "Soviet vodka". First, it is very unusual to call vodka "Soviet" rather than Russian. Then, it is very unheard of for Soviet people to drink vodka casually while roaming around the house. It was taken in shots, at the dinner table, with toasts and food.