There are several shots at MCRD (San Diego), and of the battalion marching with African-American Marines in the ranks. In 1942 and 1943, integrated units did not exist. It wasn't until 1948 that President Truman signed an Executive Order to investigate full integration of the armed forces.
Although the story takes place in 1942, all of the women's clothing and hairstyles, particularly those of Nancy Olson, Dorothy Malone and Mona Freeman, are strictly 1954; the sole exception is Anne Francis, whose appearance does actually imply the correct era at least to some extent.
When the marines arrive in New Zealand they are seen marching away from the transports that brought them. The ship to the right is marked APA-208 which would make her the U.S.S. Talladega. The Talladega wasn't commissioned until 31 October 1944, two years after Guadalcanal.
Danny and Kathy make a surprise announcement to their parents in Baltimore that they eloped overnight and were "married in Elkton." While Elkton, Maryland was widely known throughout the Northeast as a spot for quick weddings during the 1920s and 1930s, after 1938 state law required a 48-hr waiting period between issuance of a marriage license and a wedding. Thus, during WWII they could not have eloped without advance planning.
The attack transport USS Pickaway (APA-222) shown at dock side after Pat and Andy's wedding and just before the battle of Tarawa, wasn't commissioned until Dec 12 1944. This ship wasn't yet built for Tarawa.
When the unit arrives at Guadalcanal, as they march off some of the men in the first group have wet trousers from the landing on the beach, but the men in the second group have completely dry trousers.
When the unit first comes under enemy air attack, the path of explosions on the ground take a sharp turn from the left to follow the men along the road. It is physically impossible for any plane to turn sharply enough to leave that sharp a pattern on the ground
When Andy Hookins chops down the tree in front of Pat's house, he visibly "chops" it with an axe, but when the tree falls the camera pulls back to show the tree falling from a perfectly smooth stump, obviously cut with a chainsaw.