The Skeleton in the Closet - S3-E3
Corrected entry: Throughout this episode, Sir Humphrey is worried about a slip-up he made 30 years earlier being discovered when the files are released under the Thirty Year Rule. Hacker gets Humphrey to admit the fault was his, then agrees to help him cover it up. At this point Humphrey produces a document which basically allows them to empty all the embarassing papers out of the file and leave it empty. The plot hole is: Why was Humphrey so worried about being found out? He didn't need Hacker's help to avoid being discovered. He could have emptied the file without Hacker's knowledge and there's no way anyone could have known. Humphrey even stated it was normal practice for files to be emptied to avoid embarassment, so it would have been nothing out of the ordinary anyway. This would have actually worked out better for both men, as any inquiry would have drawn a blank, leaving Humphrey in the clear, and Hacker would have been able to honestly deny any complicity or knowledge of a cover up. In previous and future episodes, Sir Humphrey is more than clever and devious enough to cover up his own mistakes, even minor ones. It makes it a plot hole that his biggest blunder worries him so much when he had a solution all along.
Correction: Did you actually watch this episode? An important plot device is that the file lands on Hacker's desk BEFORE Humphrey has a chance to get rid of the evidence, and while Hacker has no intention of releasing the information he is going to use it to make Humphrey squirm while he has the chance. It's all about one-upmanship between the two men, a consistent theme in the show.
I did watch the episode, and at no time is Hacker actually in possession of the file. It hasn't landed on his desk, nor has it been released from the archives yet. The whole point of the episode is that it is SOON to be released for the first time in 30 years. So Hacker hasn't seen any of the embarrassing / incriminating documents against Sir Humphrey. All Hacker knew for a fact was that Humphrey had been a junior official in the responsible department at around the right time. It was pretty evident that given Humphrey's shifty behaviour after learning it was all about to come out, that he was the official at fault, but the file still hadn't been released from the archive yet, and Humphrey still had the means to solve the problem without Hacker's help. The plot hole stands.