Factual error: Secretary of State John Hay is depicted issuing the order to "initiate hostilities" against Spain. Unfortunately, at the time we actually went to war with Spain, John Hay was not the Secretary of State. That position was held by William. R. Day. Hay did not become SofS until September of 1898, after most hostilities had ended.
Continuity mistake: When the Spanish and German defenders of San Juan hill are loading their Maxim machine guns, the cartridge belt is being inserted from the left side. During the fighting, the cartridges are entering the chamber from the right, and the expended belt is exiting on the left.
Factual error: When Hay is authorized by President McKinley to commence offensive operations, he hands the order to a Naval officer, saying, "Pass this along, Admiral." The officer in question is wearing the uniform of a Naval captain.