In the prologue of the movie, look carefully at the German helmet on the shelf in Willie's bedroom. It is actually a modified Spanish helmet. German and Spanish helmets are the exact same shape and size but the Spanish version has extra rivets on the outer shell and a totally different liner.
When the boys scrimmage with a football, Willie's jeans have an elastic waistband in back (at around 11 mins), which would not be possible during the wartime rubber shortage. In the 1930's lingerie began appearing with elastic, but it was unavailable during the war.
When Willie Morris (Frankie Muniz) is in the woods with his Dad Jack (Kevin Bacon) and Skip and they hear a gunshot from hunters, Jack pushes Willie down and says to take a knee while hollering to the hunters, "Hello! Over here at 3 o'clock!" Only problem is, they don't know which direction the hunters are facing, so they have no idea where they are in relation to the hunters. Saying "3 o'clock" is totally irrelevant, only the sound of their voice gives the hunters knowledge of their direction.
When Willie and Skip first go to the movies, there is a girl and two boys sitting on the front row. After the camera cuts to a different shot and then back, the two boys have been replaced by 2 more girls.
During the "opening day" baseball game, a close-up of the scoreboard shows the visiting team with 2 runs in the 3rd inning (at around 36 mins). When the scene switches to a longer view (at around 39 mins), the scoreboard shows the visiting team with only 1 run in the 3rd inning.
When Willie is in school and the class is having Show And Tell, the date on the chalkboard says Sept. 27, 1942, which is a Sunday. And the calendar hanging over the chalkboard shows a month with the last day being a Monday. September 1942 ends on a Wednesday.
Dink is shown leaving for the war in 1942 wearing the insignia of the U.S. 65th Infantry Division, and later writes home from France. The 65th Division was a Pennsylvania unit, and did not deploy overseas until January 1945 and was not in combat until March 1945.