At 0:18:44 into the film, set around 1906, there is a shot of a locomotive in the countryside, which is a Class 5 Stanier painted in British Rail green with the British Rail emblem on its tender. This logo was originally LMS built around 1935.
At around 18 minutes into the movie, a train was shown steaming in the English country side, the train is in British Rail green with a British Rail insignia on the tender. British Railway didn't exist until 1948.
When Major Fawcett is preparing to leave on his first expedition, his wife tells him that she is having another child. When he arrives in Amazonia, he tells his crew that the river will be their home for two years. Yet when he returns to England, the baby is only a few months old.
Thoughout the movie the English main character communicates to the Indigenous natives with the dialect of Spanish. Considering that the natives have not come into contact with 'the white man' before, there is no way that they could have learnt this language and therefore understand him.
At 1:35:42 a soldier can be seen bringing a cigarette up to his mouth, you can see that the cigarette has a white filter. Cigarette filters were not invented till 1925, nine years after the time period the film takes place in.
During the battle scene taking place in 1918 in which Percival Fawcett got wounded you see German machine gun nest with soldiers wearing Pickelhaube (spiked helmet). The Pickelhaube was replaced in 1916 by the Stahlhelm since this was better suited in the demanding conditions of trench warfare.
Percy Fawcett is in the artillery, but his red uniform is actually meant for infantry soldiers. This was intentional, as the director liked the way the colors worked and allowed him to plausibly put Fawcett in the trenches in World War I later on.
(At around 31 mins) There's another raft docked on the shore with one man in it, and another on the shore clearly visible on the left extreme on the screen, leading a horse away. he's dressed in a shirt, blue jeans and cap.
The closed captions are incorrect in a number of places, most egregiously at 1:21:08, when the typist says, "It looks like a war with Fritz [meaning Germany]", which is captioned as, "It looks like a war with France." France and England, of course, were allies during WWI.
If both Percy and Nina Fawcett (played by Charlie Hunnam and Sienna Miller) have got blue eyes, then all their children should have blue eyes too - since that phenotypic characteristic is granted by a pair of recessive alleles, the descendants are homozygous with respect to the eye-colour gene (which is necessarily for blue), hence Jack Fawcett (Tom Holland) "should" have blue eyes.
However, 2 blue-eyed parents can have a brown-eyed child if one parent has a working gene HERC2 & the other has a working gene OCA2. Brown eyes are HERC2+OCA2, a combination absolutely possible w/2 blue-eyed parents as persons with blue eyes can be carriers of one of these working genes. See genetics.thetech.org/how-blue-eyed-parents-can-have-brown-eyed-children .