When Yakov first reads the note from Leza we can see it says "They are trying to kill you. Don't go near the barn." Later, when the woodchopper reads it he says "Don't go near the barn. They are trying to kill you."
When Georgi sees the twins together for the second time, the same shot is used from the first time he sees them. This is evident as the background is different (the fireplace should be in the background in the second shot and it is not) and there is a girl, on the left of screen in the close shot, who is not there in the longer shot.
When the Mayor tells Kovatch to give the Inspector General his uniform, he does. In the next scene, when Georgi come out of the front door, it fits him to his form. There is no way that a uniform fitting a rotund Kovatch would fit a slim Inspector General without massive alterations.
Poor editing (redundancy): When Yakov is first hawking his elixir, and about to reveal Danny's "head" on the serving plate, he picks it up and turns in a far shot, and then immediately, in a closer shot, it shows almost exactly the same motion.
In the scene when Georgi first arrives at the village, his position in relation to the soldiers sitting around the table changes between shots. Also the amount of light and shadow on the soldiers varies, with them being in shadow, partial sunlight and full sunlight at different times.
When Danny sings the gypsy drinking song, he waves around an obviously empty wine glass in the long shot. The glass is half full of wine in the close-up, when he is in no danger of spilling it.