Russian soldiers that we see in the Murmansk bar, where Captain Mike tells about fly-birds, are wearing an impossible uniform: mixture of tsarist, pre-1917 era and of the Soviet uniform created in 1943. In 1941, when the action takes place, Soviet soldiers hadn't yet shoulder boards.
There are several shots of Daisy dancing. The execution of the ballet, however, is very modern and athletic, with long extensions and high arabesques. It was not appropriate for the time period, when ballet had a very different style.
The film seems to ignore the prohibition of alcohol from 1920-1932. It was only after prohibition that bourbon was widely available; prior to giving world-wide distribution of rye whiskey to Canada, when whiskey cocktails were made it was normally with the rye whiskey made by US distilleries. The original "Sazerac" was created in New Orleans in 1859 and named by John Stiller who owned the Sazerac Coffee House.
Benjamin is seen tinkering with an Enfield Bullet motorcycle. But it contains a "Black letter on White" number-plate. "Black on White" were introduced for private vehicles only by 2000. Earlier "Black on White" plates were for taxis; private vehicles had "White on black" plates.
When Thomas Button first is seen in the movie observing Benjamin during an outdoor gathering at the old folks house, he gets immediately into his car and leaves, the camera pans back to Benjamin with a power pole visible behind him. The pole has a modern cable television/internet wire running down it, just above his shoulder.
In the wharf scene when Benjamin joins the tugboat crew, two bridges are visible in the background. This event is prior to World War II. The first of these bridges was constructed beginning in 1954 and opened in 1958. The second was begun in 1981 and opened in 1988. Neither was there prior to World War II.
Benjamin is sailing his father's sailboat on Lake Pontchartrain about 1962. It is a classic wooden vessel correct for the time period but has been outfitted with modern Harken brand ball bearing blocks (pulleys) that hadn't been invented yet. Harken blocks were introduced in 1968 for small racing dinghies. The type needed for a keel boat of that size weren't marketed until the early 70s.
When Benjamin goes to see Daisy dance in Carousel in New York, he arrives during Daisy's ballet sequence. This dance sequence does not take place until the middle of Act 2 of "Carousel." So Benjamin missed about 3/4 of the performance.
Oti is referred to as a pygmy and refers to madjembe (a pygmy word for intestinal worms) which places him as a native of The Congo or Central African Republic. However, he tells Benjamin that his country has been divided by the English and Dutch. The [now: Democratic Republic of] Congo and Central African Republic were only colonized by Belgium and France respectively, while Great Britain and The Netherlands colonized South Africa.
When Thomas Button puts newborn Benjamin on the steps of the nursing home he leaves some bills of cash inside the baby blanket, but in the next scene when Queenie pulls back the blanket the money has disappeared. Since the cash was placed inside the fold of the blanket where Benjamin's face is, the bills should have been clearly visible or at least have dropped out of the blanket when Queenie exposes the baby's face.
A maroon 1963 Pontiac Starchief appears outside the dance studio shortly after it opens. It later passes Benjamin and Daisy while they ride the streetcar. It is seen once more passing by on the street as they celebrate Caroline's 1st birthday (in 1969).
When Benjamin and Elizabeth Abbott are having their first tea encounter all the scenes that show the face of Elizabeth the glass appears to be be almost empty. When they show Benjamin's face her glass is nearly full of tea.
As Benjamin and Daisy are (according to the narration) sailing in the Florida Keys there is a quick shot of a rocket ascending. However, the NASA launch facility is in Cape Canaveral on the Atlantic coast of Florida - hundreds of miles northeast of the Keys.
Benjamin is in Murmansk in late November/early December based on the radio report of the attack on Pearl Harbor. However, he sits with Elizabeth Abbott (Tilda Swinton) until dawn. Murmansk, presently the largest city above the Arctic Circle, would be in polar nights with 24 hours of darkness at that time of the year. There would be no sunshine. The same for when the tugboat crew left shortly after the 7th with sunlight streaming in the windows.
Soldiers in the First World War would not be issued their weapons until they arrived near the front. They certainly wouldn't carry them when saying goodbye to their family when boarding the train to embarkation.
Benjamin spends a few idyllic weeks in Murmansk in December 1941 (there he hears the news about Pearl Harbor). But in June 1941 Russia was invaded by Germany. As one of the main bases of the Soviet navy, Murmansk was constantly under ferocious attacks, up until October 1944. So in no way could it be as peaceful and quiet there as we see in the movie.
From the Tug, we can clearly see tracer fire coming from the submarine. The pyrotechnic charge in a tracer round is in the base and is designed to be clearly visible to the gunner but not to the target.
Theodore Roosevelt is shown at a dedication for a clock in New Orleans' Union Station in November 1918. This event is unlikely to have occurred; according to his NY Times obituary, he was hospitalized during that time for rheumatism before he died of a pulmonary embolism in January 1919.
As Benjamin watches Daisy in the ballet, he says via narration he'd never seen New York before that. Earlier in the film as he describes his tugboat route, the Statue of Liberty can clearly be seen in the background. However, this indicates he only saw New York in passing.
When talking about how the tugboat has been commissioned into the US Navy the day right after Pearl Harbor (Dec 8, 1941), the captain says "We will fight the Japs and the Hun". The Hun refers to the Germans, but they didn't declare war on the US until Dec 11, 1941. However the Captain is Irish so would probably count 1939 as the start of the war not just when America joined it in 1941.
The majority of the story is narrated by Benjamin, or at least written down in his diary. However, the entire 'butterfly effect' scene which he narrates as a prelude to informing us about Daisy's injury contains a number of assumptions and details that he would not have been privy to - the cab driver stopping for coffee, the gift not being wrapped etc. In this scene the narrator assumes omniscience and is not consistent with the rest of the narrative.
Daisy and Benjamin's daughter Caroline was born in 1969. But when Benjamin visits Daisy at the dance studio in 1980, Daisy claims that Caroline is now twelve years old. If she were born in 1969 she would be eleven.
The goof items below may give away important plot points.
During the sequence after Benjamin leaves Daisy and their young daughter and travels through India, Benjamin is shown in front of a building which prominently features the phrase "ISO 9002". Based on the time sequence of the movie, this would be in the very late 1970s or perhaps 1980. ISO 9002 is among the internationally-recognized quality management certifications that were first introduced in 1987.
When the analog clock is being taken down in 2002 and replaced by a digital one, an ad for the U.S. Army National Guard is shown bearing the "Citizen/Soldier" advertisement which was introduced in late 2007.
The characters of Benjamin and Daisy both have blue eyes (a recessive trait), yet they have a daughter with brown eyes (a dominant trait). Biology tells you that two people with a recessive trait can have a child with a dominant trait when multiple alleles are involved.
In a scene from the hospital, Ben's daughter sees all the postcards and realises that he sent her a birthday postcard in 1981 when she "was 13" and she quotes from it before it links to a corresponding event in India. This is followed by a scene where a 'younger' (looking), and thereby 'older', Ben visits them at the dance school and Daisy tells Ben that their daughter is now "12". This could only be possible if he visited the school before he went to India, but if Ben is 'younger' then it must be after he got back.