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.
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 CElticc 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.
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.