Bugle call used in Houston's camp was the more modern "To the Color", which doesn't appear in the US Army manuals until the 1880's.
And the only musicians Houston had was a fife and drum, who played "Come to the Bower" during the battle of San Jacinto.
Several characters (Gator Davis for one) are shown wearing hats with feathers from a ring-necked pheasant. This entire episode takes place in 1836, but ring-necked pheasants are not native to North America and were not introduced here until the 1880s.
Susanna Dickinson is shown being attacked by Native Americans (unaccountably dressed like the Dakota tribe) while in the custody of the Mexican army. Actually, she was returned peacefully to the Texians. Besides, the Tonkawa tribe that occupied the area were allied with the Europeans against the Cherokee, so it's highly unlikely that they would have attacked settlers.