When Robert Ford is working in the general store, a bicycle leans against the wall. It's supposed a Highwheel, Ordinary, or Pennyfarthing bike. However, it's a contemporary model, intended for use by circus and parade riders, and only superficially similar to a period bike.
When Bob sends a telegram announcing that he has killed Jesse James, he goes into an American Telegraph Company office and uses an American Telegraph blank. American Telegraph merged with Western Union in 1866. The blank correctly identifies E. S. Sanford as American Telegraph's president, but the date (1882) is fake. Furthermore, 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 during the night, one gang member recites a poem of Catullus ("My love says she would marry only me ..."); the words he recites are from a translation published in 1970, "Catullus: The Complete Poems for American Readers", by Reney Myers and Robert J. Ormsby.
When the photographer photographs Jessie James's corpse, he replaces the lens cap on the camera and then thanks everyone for standing still. He then removes the film holder from the back of the camera and doesn't insert a dark slide to protect the sheet of film. Either the film would have gotten ruined, or if the dark-slide wasn't removed before taking the photo, no image would have been recorded.
Arguably, the term "motor" was not widely used. It was defined as, "machine that supplies motive power" in 1856. To engineers, it is a term for machines that are electrically or tension-fed (as in springs) and "engines" supplied by chemical means or processes (internal combustion or steam). At that time, the only commonly known use of "motors" is in toys...which may be why Jesse (or the culture at the time) used the term, "motor" for what is happening inside a person's (Robert, in this case) head--including the mention of gears.
In the scene where Jesse is planning the Platte robbery, Jesse refers to Robert's fear as, "motor." (Arguably), the term should have been more closer to Jesse's experience by referring Roberts fear as, "engine" because the most common "machine that supplies motive power" that Jesse has the most familiarity with would be the steam engine. "Motor" and "engine" have been misused so much that they are now interchangeable in the dictionary.
When Jesse is shot by Robert Ford, his wife is laying over him screaming and crying. The whole while Jesse's eyes are closed, at one point they cut to Robert, and cut back, Jesse's eyes are clearly wide open. They cut back and away once more and his eyes are closed again. (Possibly deliberate choice by filmmakers, to indicate Ford's state of mind.)
When Dick Liddil awakens 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 of the ice you can see the brushed away snow and a fish swimming under the ice, yet there is no evidence of the 3 shots Jesse fired into that spot.
In every scene where Jesse smokes a cigar, the length of the cigar as well as the size of the ash at the foot of the cigar varies tremendously across shots. Such variation cannot be accounted for by normal burning off of the cigar as one smokes it.
Early in the movie when the gang are sitting around in the woods talking, the shotgun one of the men is holding spontaneously disappears and reappears between a shot. Also, during the same sequence he is seen holding it in at least two different ways between shots.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
At the end of the film, we see Robert Ford in his saloon / dance hall, "Ford's Exchange", which is an actual brick-and-mortar building. Later, when he is shot soon after by Edward O'Kelley, again in his own establishment, it is suddenly a tent saloon. This is because Ford's dance hall had been burned down in a town fire, three days prior to his shooting. In real life, Ford created this temporary location to operate out of while waiting to rebuild the dance hall seen earlier.