The cars in the moving train are a different color and design and are in much better condition than the cars the Kharacter family is seen boarding.
In 1918-1919, young Liza holds a newspaper with a headline about Lenin's death; in the next shot, she reads a newspaper with a headline about the U.S. Black Tuesday stock market crash, while saying in voiceover that 10 years have passed and she is now 19 years old. In reality, Lenin passed away in January of 1924 and the U.S. stock market crash occurred in October of 1929, less than 6 years later.
Atypically old, overweight, and/or neatly-groomed soldiers throughout.
English-language signs on buildings and in shop windows in "Paris" and "Moscow" (actually Main Street in Denison, Texas, USA).
The airliner that flies Liza to Israel has Star of David markings but a U.S. "N" registration number prefix. Most countries require airlines to register aircraft in the home country, and aircraft in independent Israel use a "4X" prefix (e.g. 4X-ABC), while aircraft in British Mandatory Palestine used a "VQ-P" prefix (e.g. VQ-PAB).
The Bolshevik Revolution is portrayed as occurring in 1918. In reality, it occurred in 1917.
Obvious models whenever flying airplanes or moving trains are shown and in most Kursk tank battle footage; poor color-matching between the model-tank shots and the live-action shots throughout the Kursk battle.
When Liza flees the train station and encounters the Soviet Fifth Army, most close-up shots in the ensuing battle sequence are reversed, as evidenced by the backwards numbers on the tank turrets and the submachine gun magazines, and the rifle bolt handles being on the wrong side (the Soviet Mosin-Nagant rifle was never produced in a left-handed configuration). Additionally, the Soviet troops flee to the right in close-up, but in the long-distance shots, they flee to the left.
When Sonya and Jonathon travel to Palestine, they are obviously not actually aboard a ship, as evidenced by the concrete walls.
Obvious CGI muzzle flashes, fires, and explosions throughout.
Poor composition of the green-screen shot when the Kharacter family boards the train; the train car on the left appears too large and the floor levels do not match. (Passenger train cars are always built with uniform floor levels to ensure that boarding platforms and adjacent-car floors will always line up.)
The Ukrainian mansion has a modern electric doorbell when the Kharacter family arrives in 1918. (Despite this, characters always knock.)
There are multiple Raggedy Ann dolls in the doll room when the Kharacter family arrives at the mansion in 1918. This is the same year that Raggedy Ann character dolls and books were introduced in the United States; in the less-interconnected early 20th century world, it is highly implausible that a U.S. toy would appear in culturally disparate and geographically distant Ukraine so soon after its introduction.