In a scene which takes place in 1905, a US flag is seen with 50 stars. The correct flag would have 45 Stars.
American soldiers wear gas masks, which were not used by troops until WWI. In the US Army, they appeared first in 1917.
In scenes that take place in 1885, the cadets are carrying Mosin-Nagant rifles. This rifle did not exist at the time. It was introduced into service in 1891. The standard Russian infantry arm in the 1880's was the Berdan rifle.