Another song played at the Convention is "Hail, Hail, the Gang's All Here" from the song "Alabama Jubilee," written in 1915 and based on the chorus of "With Cat-Like Tread," ("Come Friends Who Plough The Sea") from Gilbert and Sullivan's 'Pirates of Penzance', written in 1879. Since the "Pirates" chorus would not have been played in a convention, this references a "Hail! Hail!" usage when the piece was written later than the action of the film.
Dutton Peabody was a little lax in his typesetting. The SHINEBONE STAR newspaper Rance Stoddard complimented Peabody on ("Cattlemen Fight Statehood") was VOL XXX, No. 42. Then many weeks (or months) later at the election of delegates Liberty Valance picks up a newspaper ("Two Homesteaders Killed By Liberty Valance and Gang") which also carries the same VOL. XXX, No 42.
Toward the end when the Stoddards are back to pay respects to Tom Doniphon, Rance snaps his watch cover shut and puts it in his vest pocket. He then enters the room and is snapping it shut and putting it in his vest pocket again.
When Tom enters the kitchen as Hallie is tending to Rance's wound and when he starts getting drunk his shirt is dark (probably Wayne's favorite blue, if the movie were in color). When he arrives at his ranch, the shirt is now much lighter (possibly red if in color.)
When we see Liberty Valance shot the first time in the film, he stands up with his left leg stepping on the boardwalk and then brings his right leg over his left leg, stepping actually on the boardwalk. On the "replay," Valance swings his right leg over his left, steps right into the street, and falls slightly forward without touching the boardwalk with his right leg at all.
When Tom Doniphon enters the room that the territorial convention is held, we can see several women watching the convention from outside the room. However, later when Tom and Ransom Stoddard leave the room (and when Ransom re-enters the room), the women are gone.
When Tom arrives drunk at the dream house and staggers in, his shirt is light gray. Once he's inside and lights the lantern, his shirt is black. Then in the scene where Pompey rescues Tom from the burning house, when he first lays Tom on the buckboard, Tom's shirt is light gray again. When Tom tells Pompey to get the horses, it's clearly light gray. Then after Pompey frees the horses and the camera cuts back to Tom in the back of the buckboard, his shirt is clean and black once again.
When Ransom Stoddard is found and brought to the Swedish innkeepers, Nora makes him drink "Swedish aquavit", but in fact she offers him "Rød Aalborg" (translates: Red Aalborg) which is a Danish aquavit.
In the flashback, Tom Doniphon tells Stoddard that he killed Liberty Valance, it is Stoddard who shoots first, than Doniphon. But since we've been shown that Stoddard can't hit the broad side of a barn (and in fact, his aim is wild), Doniphon's probably right.
In the last scene on the train, as Stewart is returning to Washington with his wife, the scenery outside the train repeats two and a half times...including a painted crosswalk which is unlikely to have existed at that time in a rural area.
During the train ride back with Stoddard and his wife, the scenery is going by so fast that it is hardly recognizable, however the conductor states that they'll be there in no time because they'll be going 25mph. At 25 mph you could easily view the countryside. Additionally, as the conductor was talking with Stoddad he was perfectly still, no swaying back and forth, as anyone would've done on a train in the 1800s.