The San Patricio Flag is taken from the hands of a fallen soldier, yet in a close up shot after the battle the flag can be seen under the head and hands of the fallen soldier.
When Sgt Riley is asking the Capt for permission to go to mass, his shoulder strap is over his right shoulder. After leaving the office, his shoulder strap is over his left shoulder.
There are a number of geographical and historical errors in this film, including some scenes in the battle of Churubusco (the last battle in the movie).
General Winfield Scott, commanding general of the American forces, is shown wearing three stars on his epaulets signifying the rank of a Lieutenant General. At the time of the Mexican War (1846-1848) he wore the two stars of a Major General which was the highest rank in the United States Army at the time. He wouldn't wear three stars until 1856 when he was promoted to Lieutenant General, becoming the first American since George Washington to hold that rank.
The type of noose used to hang the men was of 1880s design, intended to break the neck of the prisoner as opposed to strangling them, where a slip-knot was used. Since the execution did not drop them from enough height, the noose would not have worked, even if it had existed.