On the bus arriving at the Marine base at the beginning of the movie, California is misspelled "Caliornia."
Gunnery Sergeant Watrous was wearing Master Sergeant stripes on his uniform which is one rank above Gunnery Sergeant. Not a goof: In 1941, the insignia with 3 chevrons and 3 rockers was a Master Gunnery Sergeant, as well as Sergeant Major.
Cliff Harper says that he and CPL Tabeshaw have been together ever since boot camp back in 'Dago while they were actually on MCRD San Diego when he said it.
When the Marines are leaving the building in San Diego, there is a parade on the deck and the band is playing the Marine Hymn. By tradition, all Marines, whether in or out of uniform, turn to face the music at the position of attention. Yet the Marines leaving the building continue on their way without stopping.