Bertha tells her parents that the baby is named Alexander Murray Palmer Haley and this was indeed the real Alex Haley's full name. The Murray is for his maternal grandmother's family and was in turn taken from the family to whom they belonged as slaves until the end of the Civil War. However, in Roots (1977), the owners were named Harvey so this should have been one of the baby's names.
Andy Warner is running for re-election to the House of Representatives after Simon Haley returns from World War I. However, the war ended on November 11, 1918, six days after the 1918 Congressional elections.
The helmets used by the German soldiers during the battle scenes were incorrect, the helmet used in the episode was the M40 (Possibly M35) Stahlhelm, the correct Stahlhelm for the time would've been the M16-18 variants.
When Haley's patrol encounters a German machine nest, the Germans are firing a WWII era MG42, an air cooled machine gun. Machine guns of this era for the most part were liquid cooled.