When Lafitte and his men are fighting the Indians near the beach, many of the Indians are wearing buckskin breeches, have headbands with feathers stuck in them and their hair is in pigtails. Those are styles and clothing worn by the Plains Indians of the Southwest in the middle and late 1880s, not Indians on the coast of the Gulf of Mexico in the early 1820s.
When the Indians attack, a pair of them jump up on a log, one gets shot, and the other gets stuck with a pirate sword and falls backward. Except he clearly doesn't get stuck with the sword, the sword doesn't even come close to him.
The earliest known version of the song, "I Wish I Was Single Again", was around 1904, which is much later than the setting of the film.
In the movie, Galveston Island is presented as hilly and wooded. Until a seawall was built about 1910, Galveston Island was basically a flat sandbar. Even today, no place on the Island is more than 15 feet above sea level.