Besides being a feared and well-respected lawman, Bucky O'Neill had also been an Indian scout and the Mayor of Prescott, Arizona, as well as a self-educated, very well-read and multi-lingual man (speaking French, Spanish and several Indian languages). He and Roosevelt became fast friends and spent much of their time in the campaign discussing military history, Indian customs and classic European literature.
Real casualties of the Rough Riders was 40% and many died from malaria, after the battle because the US would not let them back into the country, finally TR was able to get them back to Montauk New York in a quarantine camp. On the Library of Congress American Memory website, there are early Edison movies of them at the Montauk quarantine camp.
Roosevelt's encounter with Senator Mark Hanna and the French woman Mademoiselle Adler (who loses her flower to Roosevelt's gesticulations) at the dinner party is inspired by a real-life incident, although Roosevelt's wife and Colonel Wood were not present. Much of Hanna's dialogue in the scene - "We'd be at war with half the world if you were President!" - was not actually said to Roosevelt, but to Adler after they left the party (as recorded in her diary).
There are land crabs in Cuba that might be attracted to a 19th century field hospital, but the crab that Nash kicks away from his leg wound is a coastal blue crab that would *never* leave the water voluntarily.