The Late Inspector General - S1-E4
Plot hole: At the beginning, the Inspector General instantly pegs the incidents Hogan's men enact as staged to defame Klink, and takes it as proof Klink is the right man to be put in charge of all POW camps in the Reich. Later, as Klink and he do their "final inspection", much less severe - and frankly, much less believable - incidents cause him to completely revise his assessment of Klink. Him believing Klink would be a pickpocket and compulsive kleptomaniac simply doesn't make sense.
The Late Inspector General - S1-E4
Other mistake: While the General is in Klink's office making the recommendation for Klink to be commandant of all German POW camps, he mistakenly calls Stalag 13, Camp 13 three different times. Camp 13 was referenced in the black and white pilot episode.
Suggested correction: Stalag is short for "Stammlager." "Lager" is the German word for "camp." (To avoid unnecessary discussions: depending on the context, "Lager" can also mean stash, cache, storage, warehouse, bedding or bearing, but in this context it is indubitably to be translated as camp). So "Camp 13" is absolutely correct in this context.