When Captain America's ice-encased shield is revealed in the beginning of the movie, the paint job is pristine with no damage. However, in the final fight with the Red Skull, the shield is seen to have numerous dings and scores in the paint from bullet strikes.
Sign warning "it is illegal to falsify enlistment form" is not on wall as next enlistee after Rogers enters exam room at the fair.
(at around 1h 5 mins) After Schmidt reveals his true face in the Hydra base to Captain America, the two begin their first fight scene. It's here that Red Skull displays his super strength and punches Captain America's steel shield leaving a fist impression in the metal. The two keep fighting but the fist impression is no longer on the shield. Later at HQ, when Stark pats the shield and remarks how Rogers is attached to it, the punch impression is there again.
(at around 35 mins) Before Steve Rogers is sealed into the pod for his transformation into a super-soldier, two metal arms with several hoses are pivoted over his shoulders to hold pads against his chest. When the pod opens after the transformation, the arms have disappeared. Nor are they detached and dangling from the hoses, which have also disappeared. There is insufficient space within the pod for the arms to retract in any manner. However, mounting studs for the arms are visible.
While the 1st Hydra base encountered is self destructing and the bar Barnes just went over falls down it can clearly be seen the railing is still intact, then a few cuts later it is broken.
Captain Steve Rogers wears the yellow American Defense Service ribbon. The ribbon/medal was awarded for qualifying service performed between September 8, 1939, and December 7, 1941. Since Rogers joined the Army after America's entry into WWII, he would not be entitled to wear this ribbon.
(at around 1h 12 mins) The Union Flag hanging outside the War rooms is upside down. At the flagstaff, the white Saltire of St. Andrew (Scotland) takes precedence over the red Cross of St. Patrick (Ireland) because Scotland has been part of the Union longer than Ireland, i.e. at the flagstaff the white diagonal band must be thicker above the red diagonal. While many countries fly their flag upside down in times of war, the United Kingdom is not one of them.
(at around 1h 9 mins) During WW2 if a soldier/sailor/marine did not come back from a mission, he was initially declared "Missing in Action" (MIA). Only later would he be listed as "Killed in Action" (KIA). Sometimes this occurred long after WW2 ended.
(at around 30 mins) When Steve and Peggy pull up to the antique store in Brooklyn, there is no gas ration stamp affixed to the windshield of their car or any of the other cars.
If Vibranium is "vibration proof" the bullets striking it would make no ringing sound.
Some have considered it a goof that the Hydra logo (a skull and six tentacles) incorrectly portrays a mythical hydra, which would be a multi-headed creature. The logo is the same as the one used by the Hydra organization in the Marvel comic books. Although the organization's name and motto ("cut off one head and two more will appear/cut down one of us and two more will take his place") are based on the mythical creature, the logo is not intended to represent a hydra. The skull represents it's founder, the Red Skull (and conveniently, death). The six tentacles represent that it is an underground group that believes it is capable of infiltrating every human endeavor and organization. It is a symbolic logo, not a wildly inaccurate hydra, nor a six-armed octopus with a skull for a head.
(at around 46 mins) Peggy takes a sample of Steve's blood, explaining that she wants to see how his "genetic code" has been altered. This is perfectly valid both historically and in the context of the plot. The term "genetics" was coined in the early 1900s, and by 1942 scientists in a field they called "molecular genetics" already understood that there was some chemical component in a cell responsible for determining an organism's characteristics. Although DNA wouldn't be discovered until 1953, a secret research organization like SHIELD would presumably be years or decades further ahead. (See, for example, all the other fancy gadgets they use.)
(at around 11 mins) The exposition depicted in the movie is not, as some viewers have assumed, the World's Fair in New York City, which happened in 1939, much too early for the film. The characters actually attend the fictional "Modern Marvels of Tomorrow" exposition.
(at around 1h 9 mins) While chewing out Agent Carter for helping Rogers on his mission to free Bucky Barnes and other captured soldiers, Colonel Phillips leaves the tent without a helmet on. The next scene cuts to him walking outside his tent with a helmet on. While it's easy to miss, the Colonel grabs his helmet on the way out of the tent. He simply put it on as he walked.
Military units show African-Americans and appear to be integrated, but the troops were not integrated until 1948. However this is a specialty unit from a fictitious military branch, not a standard battalion.
(at around 42 mins) When Steve Rogers pulls Heinz out of his little submarine boat and throws him onto the dock - then climbing a ladder out of the water himself - both characters are dry. Their clothes are dry and no water is dripping on the ground beneath them.
(at around 10 mins) When Bucky helps Steve from a bully attack in an alley outside of the movie theater towards the beginning of the movie, he picks up Steve's failed DSS exam certificate signed and dated 14 June, 1945. The movie takes place in 1942/43, as well as the fact that Germany had unconditionally surrendered in May of 1945, ending WWII in Europe, one month before the signed date.
Steve Rogers is only told to take off his hat, tie and shirt before he gets in the Super Soldier apparatus. But after he gets boosted, his shoes and socks are now missing, as well.
(at around 40 mins) When Steve Rogers is chasing the assassin through New York City, he jumps in the air several times, revealing the soles of his feet, which always stay clean and never appear to get dirty.
(at around 1h 15 mins) Stark accidentally detonates an ammo pellet taken from one of the Red Skull's weapons while examining it in a safety chamber. Although the observation window explodes in Stark's face with enough force to blow him across the room, the only injury he suffers is a small cut over his right eyebrow.
(at around 1h 55 mins) James Payton is credited as playing "Adolph Hitler". The correct spelling is Adolf Hitler.
When COL Phillips is talking to CPT America after the POW rescue, the eagle of his rank on his collar is facing to the left, while the eagle on his helmet is facing to the right.
When Agent Carter shoots at the yellow cab near the beginning of the movie, she does it from behind the vehicle. They show two holes through the windshield, but only one through the rear window.
At one point, while Schmidt is speaking to Zola, he says the word "victory", pronouncing it as "wictory". This would not be a German pronunciation. In German, a "v" is pronounce as an "f", so he should have said "fictory". The language consultants should caught this error.
(at around 1h 30 mins) The map behind Colonel Phillips at the last briefing depicts modern-day Canada, all in the same color. Newfoundland and Labrador didn't join Canada until 1949; before then, it was a separate Dominion ruled directly from London.
A map shows the allied positions close to the Italian/Austrian Border. By 1943 when the film is set, they hadn't even taken Rome yet, which fell in June 1944. They would not even come close to the border until November 1944.
(at around 1h 29 mins) When Steve Rogers and Carter are sat in a bombed out pub in London during an air raid, a rather modern sounding two tone emergency services vehicle siren can be heard outside. Emergency vehicles during the 1940s used bells and this type of siren was not used until the 1970s.
(at around 25 mins) When Steve Rogers and Dr. Erskine are sitting in the barracks having a discussion, Steve's footlocker has his social security number on the lid. During World War II, military personnel had a service number which had a different format than the social security number used by today's military.
(at around 1h 12 mins) A telephone in the War Room bunker beneath London when Steve Rogers's troops deploy there for briefing is a type font not invented until the late 1960s.
(at around 1h 3 mins) When a German grenade is used a 'ping' of the striker handle being released from a 'Pineapple' style grenade is heard. The German stick grenade is ignited with a pulled cord which starts a chemical friction ignition.
(at around 3 mins) Tønsberg, Norway is depicted as having several high mountains around it. Tønsberg is actually a coastal town in a fairly flat area, with no mountains in the vicinity.
When Steve Rogers is in a war camp in Italy, an American black-capped chickadee can be heard singing.
In the secret lab, Erskine tells the audience Rogers will have the serum injected into his major muscle groups. Apparently, those only included his pecs and biceps, as those are the only injection sites shown. Despite being "saturated with Vita-Rays," one wonders how could his lats, quads, hamstrings, and glutes have responded without serum.
(at around 30 mins) When Steve and the Sgt are going to Brooklyn and the secret lab he is not wearing his garrison hat in the car. When he gets out of the car he does not put it on. He walks all the way to the doorway of the fake store and as he enters, he puts the hat on. This is not in keeping with military custom. He should have had the hat on before he got out of the car, and should have taken the hat off as he entered the store.
(at around 1h 10 mins) When Captain America salutes Colonel Phillips after coming back to the camp with the rescued soldiers, he ends the salute before the Colonel salutes back. By regulation a soldier holds a salute to a superior officer until the superior officer fully salutes back.
(at around 31 mins) When Steve Rogers arrives at the building for his transformation, he exits the car and puts on his hat prior to entering the building. He then wears the hat indoors until the procedure starts. Military personnel are required to remove their headgear while indoors unless they are armed (such as Military Police).
(at around 8 mins) When Steve Rogers wants to be signed up, the army doctor looks over his charts. Sinusitis is misspelled as Sinusitus.
(at around 1h 50 mins) During the radio broadcast of the Dodgers-Phillies game, the broadcaster mispronounces the name of Brooklyn outfielder Pete Reiser as "riser", but it should be "reeser". The broadcaster is apparently Red Barber, the Dodgers' long-time announcer, who would have known how to pronounce Reiser's name.