The setting shots to establish Barney and Andy have arrived in Raleigh are not of Raleigh at all. It's Seattle. Seattle landmarks aplenty confirm it. Even found an online article discussing how many of the landmarks in the shot are now destroyed.
Near the end, Andy and Barney walk toward the elevator while talking. The elevator door just happens to open without them even pressing the call button and they don't even pause for a moment waiting for the doors to open. It's as if they knew the elevator would open at the exact step for them to enter. [EDIT]: Sometimes a floor is accidentally selected when people depart the elevator, which would send it to a floor and open the doors without anyone hitting the call button. But in this episode, there is an elevator operator. If he wanted to get down to the first floor, the doors are going to have to open before Barney and Andy select the call button.
When Barney and CJ enter room 420, there's a large, curtained window on their immediate right. This isn't possible, since room 418's door is just to the right of room 420's door.
Andy and Barney leave town without leaving anyone in charge during their absence (not even a comment about Mayberry being safer with no one in charge than with Barney in charge) and the business with the commissioner does not require both of them.
Barney and Mr. Hasler lock the house detective inside a bedroom closet by simply turning a latch on the outside of the closet door. Closets don't normally have a lock, because the only purpose would be to keep someone inside.
Taylor and Fife are outside of their jurisdiction and shouldn't be investigating a crime nor making arrests. Raleigh law enforcement is not mentioned.
Andy goes off to police headquarters for an in-depth tour of Raleigh's modern methods, leaving Barney behind, to do nothing, at the hotel.This is completely counterintuitive to what's known about Barney, as he's always the one talking about modern methods/technology in police work and how badly Mayberry lags behind ("Why, we don't even have a helicopter!"). Barney would be the one most interested in Raleigh's modern methods, not Andy, and it makes no sense that he did not go to police HQ for a tour.