When Columbo cannot sleep in the barracks and has to make a telephone call, he gets out of bed barefoot. As he starts to walk, we hear the sound of shoes on the floor. He wears laced shoes, so he couldn't have simply slipped into them as he rose.
During the morning's cadet formation (the morning after Columbo stays overnight) the cadets present themselves in front of the Colonel for inspection. (The camera angle is shot from behind the Colonel showing the troops from the front). At the command "Dress right" the cadets should extend their left arms and look right, resulting in even column spacing; however the first cadet in the column to the Colonel's left, makes a mistake and places his left hand on his hip, then realizing his error and raises his left arm up. Additionally, this cadet is the only one that has his hat on crooked. The brim is distinctly turned to the right of his face. Also, the cadet in the second row, third column from the left, has sunglasses on. Definitely not appropriate for cadet dress formation.
When Haynes walks into the Commandant's office, in the long shot, there is a solid red furled flag with white stars (it is unclear of whether or not it is a General Officer's flag which would also be in error) over the Commandant's left shoulder but in all other shots, this flag has been replaced with the California State Flag.
As Columbo joins Rumsford for dinner, he is given a plate
with a good-sized steak, accompanied by sweetcorn, carrots and something green, all in small neat piles. A few shots later, when the assistant cadets are excused from the table, his plate is there with the steak, but absolutely piled high with peas and green beans, but no sweetcorn at all. Then when he adds bread to his plate, it has the same ingredients as the first plate.
While Columbo collects fragments of evidence and initially speaks with Col. Rumford on the parade grounds, a cadet reports that all of the cadets have been assembled in the chapel for the Colonel to address. However, in the background of the next wide shot, a unit of cadets can be seen walking along the colonnade.
In Rumford's office, after Columbo gives the Colonel a match to light his cigar and he strikes it, we see the end of the cigar in frame a few seconds later: it remains unlit. McGoohan clearly just didn't try to light it.