Miss Barnes asks Col. Madden if, after he avenges the hanging of Senor Bello, he would erect a sign in his honor quoting a Filipino poem that mentions several kinds of trees, including a cypress. Madden and his men do so, but the on the sign the word cypress is erroneously spelled "Cyprus", like the Mediterranean island.
During the climatic battle, we see Quinn crawling through the mud with his Thompson as a Japanese truck is bearing down on him. Wayne peppers the truck with machine gun fire, causing it to crash. A second later you see Quinn join up with Wayne and he's perfectly clean.
When Maximo learns of his father's death, he runs into the room and is weeping copiously, but throughout the scene, his shoulders and body never move at all, so the sounds he's supposedly making don't match his body language at all.
When we first see Miss Barnes addressing her school, she says that the agreement between the United States and the Philippines had set the date of Philippine independence for July 4, 1946. In fact, the original 1936 agreement between the two countries had set the date of Filipino independence for 1944, but the advent of World War II made it necessary to delay independence until after the war was over. The Philippines did become independent on July 4, 1946, but that was not the date set in the agreement Miss Barnes alluded to.
Imperial General Headquarters regarded Homma as not aggressive enough in war (resulting in the high cost and long delay in securing the American and Filipino forces' surrender), and too lenient with the Filipino people in peace, and he was subsequently removed from his post on June 9th 1942 and returned to Japan. In the movie when they are discussing the possibility of Filipino independence with Dalisay Delgado, Homma, would have been in Japan at this point in time.
When the Australian radio officer types the message he's receiving from the Phillippines, he spells the word "organization" using the American spelling, with a "z". An Australian would use the British spelling - "organisation", with an "s" - although, it is possible he simply wrote "z" because he was quickly transcribing the Morse Code signal sent by the Americans.
A long shot of the truck carrying the Japanese soldiers and the boy Maximo driving along the mountain road is repeated twice (the truck is seen passing in front of a hill headed toward the right of the screen, then the same shot is repeated a few seconds later).