Near the end of the movie, when Dersu gives Vova his forked walking stick, he tells the boy that he's had that stick for "many, many years." In the first half of the film Dersu's walking stick had much longer forks.
When Dersu and Arsenev are looking at the 3/4 moon and the setting sun, the moon is in the wrong phase to appear in the sky at the same time as the sun.
In the burial scene, the shadows of the actors make it clear that there is a fake backdrop.
The rifle Captain Arseniev carries is a Winchester Model 1895 musket. The Russians acquired these rifles in 1915-1916, therefore the Captain most likely would not be issued a Winchester in 1905.
In the photo where Dersu is holding a balalaika, his left hand is holding the neck of the instrument from the top, rather than from the bottom as a musician would hold it.