Twice, the film shows Jesse James dime novels as part of Robert Ford's personal Jesse James collection, which he keeps in a box under the bed at his sisters' farm. Those novels, specifically the one on top of the collection, were created in 1901.
When Robert Ford is working in the general store, the bicycle leaning against the wall is supposed to be a Highwheel (also know as Ordinary or Pennyfarthing). It's actually a modern version, intended for circus and parade riders.
When Robert Ford sends a telegram announcing that he has killed Jesse James, he goes into an American Telegraph Company office and uses an American Telegraph blank. The blank correctly identifies E. S. Sanford as American Telegraph's president, but the date (1882) is wrong. American Telegraph merged with Western Union in 1866. American Telegraph's lines ran along the Eastern seaboard, from New York to New Orleans. St. Joseph, Missouri, was in the territory of Illinois & Mississippi Telegraph Company, which later merged with Western Union.
As the gang members wait during the day to rob the train at Blue Cut that night, one gang member recites a poem by Catullus ("My love says she would marry only me ..."). The words are from "Catullus: The Complete Poems for American Readers", by Reney Myers and Robert J. Ormsby, published in 1970.
Jesse James uses the term "gunslinger" but this term didn't come into use until at least the 1920's. Terms for outlaw gunmen appropriate for the time would have been gunman, pistoleer, shootist, or even gunfighter.
The glass on Jesse James nightstand Bob Ford picks up and handles is a mid-20th century 10 sided 750 ml. Luminarc made glass. Thick durable tempered glassware and mainstay of French kitchens, the Luminarc brand was created in 1958. The typical water glass of the period would be a handmade mouth blown vessel, blown into a mold or pressed.
When the photographer photographs Jessie James's corpse, he replaces the lens cap on the camera and thanks everyone for standing still. He then removes the film holder from the back of the camera, without inserting a dark slide to protect the sheet of film. The film would have been ruined. If the dark slide wasn't removed before taking the photo, no image would have been recorded.
When Robert Ford shoots Jesse James, James's wife lays over him, screaming and crying. Jesse's eyes are closed. When the shot cuts to Ford, then back to James, his eyes are clearly wide open. After another cut away, James's eyes are closed again. (It may have been a deliberate choice by filmmakers, to indicate Ford's state of mind.)
When Dick Liddil wakes up and goes downstairs to investigate a noise, he takes a revolver from under his pillow and cocks it. A second later, as he goes down the steps by candle light, the pistol is clearly not cocked.
When Jesse James and Charley Ford cross a frozen river, Jesse wipes away the snow to check the ice thickness. He also fires 3 rounds from his revolver into the ice. In a subsequent shot the brushed away snow is visible, and a fish swims under the ice, with no evidence of the 3 shots James fired.
When Jesse James plans the Platte robbery, he refers to Robert Ford's fear as "motor." In 1856, motor was defined as a machine that supplies motive power. At the time, motors were common in toys and steam engines. It was not unusual at the time to use the term "motor" for what is happening inside a person's head.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
At the end of the film, Robert Ford in his saloon, a brick-and-mortar building. When Edward O'Kelley shoots him, he is suddenly in a tent saloon. Ford's dance hall had burned down three days earlier. Ford operated out of a tent while waiting to rebuild the saloon seen earlier.