When Jimmy first hands Nucky the envelope of money at the pier it's real bulky. Next time you see it in Nuck's hand it's flat.
Before Enoch looks in the Incubators window, we can see that the storefront has a large sign above the door. As he walks away from the storefront, the large sign has been removed.
Enoch "Nucky" Thompson was patterned after real life Atlantic City boss Enoch "Nucky" Johnson. However one crucial detail was added in the series that doesn't reflect real life: There is no evidence that Nucky ever killed anyone during his lifetime.
In the prohibition party scene at the beginning of the episode the ceiling begins to have multitudes of black latex balloons drop from it. Although latex balloons were invented in the early 1800s they were not put into mass production until the 1930s and therefore were unlikely to be available in such abundance if at all in 1920. However, they might have been procured for an extravagant and decadent party such as this one.
Charles Luciano is referred to as "Lucky" Luciano in the show. Some sources state that he didn't earn this nickname until a failed murder attempt in 1929, but other sources assert that his nickname came from his ability to avoid police in his younger days.
Al Capone tells Jimmy Darmody that he served in the "Lost Battalion" during World War I. Truth is Al Capone never served in the military.
The record Colosimo is playing on the phonograph in his restaurant just before he is killed is from the 1930's, not 1920 or before. It is an RCA Victor "Red Seal" record, in 1920 it would have been branded simply "Victor" because RCA didn't buy Victor Talking Machine Company until 1929. Also, the end of the record has a spiraling groove in the blank space around the label which was never found on records until they became electronically recorded in 1925, records before this time were recorded acoustically.
Music featured the tune "You Must Have Been a Beautiful Baby" which was not produced until 1938.
The comic strip "Gasoline Alley" was created in 1918 with the purpose of informing its readers about the upkeep of the new consumer product - automobiles. after a few years the publisher asked the strip's creator Frank King to widen the feature's appeal to women by writing in a baby for the lead character, Walt Wallet. Because WAlt was a bachelor, it was decided that he adopt a little baby that was abandoned on his doorstep. Wallet named his son "Skeezix" after a Celtic word meaning 'tyke' when he found him. Skeezix made his first appearance in "Gasoline Alley" on Valentine's Day, 1921, which is more than a year when Jimmy Darmody uses the term when referring to his son when this episode takes place in January, 1920.
Knee length flapper dresses and other costumes are from the mid to late 1920s. The pilot occurs in January, 1920, so the wardrobe should be from the late Teens.
S1E9 Belle Femme: The prisoner is being taken north from Atlantic City for safe keeping in New York. But the car is headed south as evidenced by the Atlantic Ocean on the drivers side and the Atlantic City sign behind them.