Newly crashes through the front window in making his escape, destroying the glass and mullions, but a while later one of the outlaws keeps watch through the same window miraculously restored.
When Matt Dillon arrives in the town on the stagecoach and asks for volunteers to assist in transporting his prisoner, his shirt is covered in dirt. When he subsequently enters the telegraph office across the street, the dirt is gone.
When the telegrapher is told to change the message, he does so, rather than sending the correct message (on the reasonable assumption that the bad guy doesn't know Morse code).
In the last scene, at the Longbranch, when Newly takes the telegram from Doc, he rotates it as he takes it and would be reading it upside down.