Much of the Cyrillic lettering in the film is inaccurate, as it relied on the post-Soviet version of Cyrillic rather than the version which had been used in Tsarist Russia. One of David Lean's assistants tried to point this out to him, but Lean ignored him.
In an early scene (pre-Revolution), Komarovsky says to Lara, "I want to avoid Kropotkin Street." Before the Revolution, this street was called Prechistenka. Kropotkin was an anarchist, and there would never have been a street named for him in Tsarist Russia.
In the scene where Dr. Zhivago first arrives in Moscow (near the beginning of the movie). He is boarding a tram on Tverskaya street. In the background, is a statue of Yuri Dolgoruky, the founder of Moscow in 1147. The statue was placed there in 1947 on the 800th anniversary of Moscow's founding. It wasn't there before the Bolshevik revolution, the time during which the scene is supposed to have taken place.
When a near-frozen Zhivago gets back to civilization after deserting the Red Partisans, he is almost run over by a train. After jumping out of the way, he asks a man in front of the train station where he is. The sign in Cyrillic on the station reads (due to transposed letters) "Yuryaitin", not "Yuriyatin".
Before Yuri Zhivago is about to catch the tram, Yuri Dolgoruky's statue is behind hime. In the next scene, when Zhivago starts running toward the tram, the same statue is far ahead of him. This mistake was inevitable because the street is very short and they had to move back and forth along it to make it look longer.
When Yuri, Lara and her daughter are riding in the sleigh on the way to the ice palace, the close-up shots show the three of them in the sleigh. In the wide shot where the sleigh goes over a bump, there is only one driver in the sleigh and no passengers.
The frame story (where Zhivago's half-brother finds his and Lara's daughter and tells the story) is set in the 1960s, but the daughter, who was born around 1920-1921, is only in her early 20s. In the novel, the frame story is set in World War II, which makes more sense.
After Pasha is injured by the police in a protest, he shows up at Lara's mother's place with an injury to the left side of his face. During the ensuing scene, the injury shifts to the right side of his face, then back to the left side again.
The city railroad scenes were filmed in Spain, and many of the forest railroad scenes were filmed in Finland; in both of those countries, most of the railroad track is broad gauge (the rails are more than 5 feet apart). The plains and mountains railroad scenes were largely shot in Canada, where the rails are "standard gauge": 4' 8 & 1/2" apart. The rails can be seen to jump between far apart and closer together more than once as the movie progresses.
When Yevgraf gives Tonya the book with poems, it has its author listed by initials only. He says that he's not the author and that Y. A. Zhivago stands for Yuri Andreevich Zhivago. But the book is clearly written in Cyrillic, and so Yevgraf's name starts with a letter "Ye", while Yuri's name starts with a letter "Yu", which are two different letters. Tonya couldn't possibly mistake Yevgraf for the poems' author.
The bell ringing throughout the movie is inaccurate. Bells are heard ringing randomly or even "change ringing". This was practice in western Europe, the UK, and the Americas. However, in Russia, they always used "zvon" ringing which is very rhythmic with high bells playing exactly 2 or 3 times the speed of the bass bell.
There are priests and deacons at the funeral for Yuri's mother and again at the recruiting parade where Yevgraf joins the army. At each event, the deacon is wearing his "orarion" (stole) on the wrong side. It should be buttoned to the top of the "stikharion" (robe) on the left side, not right.
When Komarovkski and Lara leave the ice palace, there is already a set of tracks in the snow in front of the sleigh, even though it had just arrived. The tracks were probably left over from a previous take.
During the scenes portraying the protest parade and the subsequent attack of the soldiers, it is supposed to be a bitterly cold night but there are no visible breath clouds from humans or horses which proves that the scenes were filmed in a warm environment. Also, observers on the balcony absently place their hands in "snow" on the railing.
In the medical teaching lab Yuri's view through the microscope is actually time-lapse footage of what appear to be moving animal cells, probably live cancer cells from culture. The movements of such cells are so slow in real time as to be virtually unnoticeable, even when magnified through a microscope.