The day after Klink takes Hogan's code book, General Burkhalter brings Colonel Sitzer to tell Klink that he is receiving the award. The code book is not visible on Klink's desk. Newkirk then reports the book is on Klink's desk. There is no point when the code book was placed on the desk, and the book is too large to have been hidden under Klink's cap (which is where the code book is located when the guys come in to steal it back).
In some of the scenes in Klink's office, production lights were reflecting off of Klink's monocle. In one scene, two lights were reflecting from different angles, one small light, then one larger light.
From the time that Hogan takes the men out of the barracks until the time that they get there for the apology, there is no time to rehearse the words. As it is given in Klink's office, they must have rehearsed it quite a bit as they did it from memory with no notes.
At some point, Klink should have recognized that the book he took from Hogan was not a hygiene book, but some sort of code book. He should not have left it on his desk for that length of time (basically overnight).
While Hogan is out delivering the package to Leslie Smyth-Beddoes, he supposedly unable to function due to a toothache. Within hours, Hogan is back up and completely healed - and Klink says nothing about it.