Corrected entry: It is explained that Captain Americas shield is made of Vibranium, and absorbs any impact and neutralises vibration as is demonstrated when Peggy shoots bullets into the shield. However, throughout the rest of the movie, Captain America throws the shield at his opponents or simply hits them with enough force to knock them out. This cannot be true, if the Vibranium absorbs the impact and vibration, then the damage inflicted on his opponents should be minimal if anything at all. Please note that Captain America hits people with both the edge of the shield and the face of it.
Corrected entry: It is explained that the Vibranium shield absorbs vibration, and when shot at, bullets fall to the ground. Surely this would mean when thrown at a wall, the shield would absorb the vibration from the impact and fall to the ground, not bounce around as it does on numerous occasions.
Corrected entry: The Red Skull's flying wing takes off from the secret base in the Alps, the ensuing fight between Captain America and the Skull and his minions takes all of 15 minutes, yet somehow the aircraft is over the Arctic. A propeller-driven aircraft simply can't reach Mach, and as a matter of fact, propellers would slow any jet aircraft down, so it would be physically impossible for the wing to travel the 4000 miles it would have had to.
Corrected entry: When Red Skull shows the Nazi officers his weapon and proceeds to kill them all the map of the "hostile" capitals shows London, Paris, Rome, Berlin and Dublin, however Dublin is actually about 100 miles further south. The pin and the name on the map are on Belfast, the capital of Northern Ireland which is part of the UK. Dublin, the capital of the Republic of Ireland, was actually neutral during WWII.
Corrected entry: The Army training scenes show African American soldiers intermingled among the troops. The Army was not integrated until after WWII.