When Andy enters Mr. Izamoto's Judo Studio, there is a Judo student in a gray sweatsuit (a young uncredited Kent McCord) leaning against the divider wall several feet in from the entry as Andy steps in and up to Mr. Izamoto. Although he is shown beginning to stand up straight in the first shot, when they cut immediately to a side shot of Andy and Mr. Izamoto, the Judo Student standing right next to them at the divider has now disappeared.
After Barney issues Fred the Ticket, and Fred tells Barney that when he sees him out of uniform he's going to beat him "to a pulp" - and grabs the knot of Barney's tie and pulls it up slightly with his right hand. Barney then has a line about being careful about he talks to an Officer of the Law - and Fred is still holding the knot. The next cut shows Fred's right hand free off Barney and using it to put the ticket into his pocket.
As Barney is writing out a ticket to Fred for littering, he looks across the street at what is presumed to be a public clock on a building and states that it was 12 o'clock. Barney then looks back at his citation book to write down the time. There are no clocks on any of the buildings in Mayberry.
When Andy sends Barney to confront Fred, he says there was a light on at the grocery. No light was on.
When Fred leaves the courthouse after paying his fine, the pedestal for studio lights or some other studio equipment is clearly visible just outside the door.
When Fred encounters Mr. Izamoto the Judo Instructor (who is dressed as and pretending to be Barney), Fred watches him walk towards him from down the street. Although short in stature like Barney, Mr. Izamoto's build does not resemble Barney's build at all. Barney's build is extremely lean and Mr. Izamoto's build is very muscular. In addition to this, his walk is entirely different from Barney's very distinctive "swagger." When they are in the fight, Fred has the opportunity to look directly at Mr. Izamoto, and although it is supposed to be dark in the alley, there is clearly enough light to see that this is not Barney.