2nd Infantry Division
The 2nd Infantry Division was activated on October 26, 1917, at Beaumont, France, after which it participated in a variety of battles during World War I.
The 2nd Infantry Division entered combat in World War II on June 7, 1944, landing at Omaha Beach. The division also participated in the liberation of Brest, France, and the Battle of the Bulge in the Ardennes.
The division would later fight in Korea in the 1950's, and returned in the mid-1960's where it remains today in a defensive posture south of the 38th parallel.
Fact vs. Fiction
A 2nd Infantry Division patch can be seen on the shoulder of Colonel I. W. Bryce, a General Staff officer. Although he would not have been a member of the 2nd Infantry Division at the time, Bryce would have been allowed to wear a former unit's patch as long as he had served with that unit in combat.* This is known as a shoulder sleeve insignia for wartime service, and is worn on the right shoulder (the left shoulder being reserved for a soldier's active unit).
Bryce also wears a World War I Victory Medal ribbon, which suggests that he served with the 2nd Infantry Division during World War I. The 2nd Infantry Division did not see combat in World War II until June 7, 1944, so it would have been virtually impossible for Bryce to have served with them, and then get shipped back to the states a few days later.
* U.S. Army Wear and Appearance of Army Uniforms and Insignia (PDF | 2.9 MB) does not indicate that soldiers who served in World War I were authorized to wear a shoulder sleeve insignia for wartime service, so it is still not clear if Bryce would have been allowed to wear a 2nd Infantry Division patch.