When the gang finds out that their trick worked and the spy in London has been caught, they are just outside the door of Barracks 2. This is the barracks they normally live in and operate out of (the BARRACKE 2 sign on the building is visible behind Hogan and Klink as they walk away from the rest of the gang to speak privately). Then, in the end segment (normally the denouement), when Schultz comes to get Hogan so he can meet with Freitag, as they walk out the barracks door, the sign on the building visible through the door is BARRACKE 2 (Barracks 2).
Hochstetter says that the 504th Bomb Group had been taken out of action and returned to the U.S. In fact, the 509th Composite Bomb Group was created from scratch and was not an existing Bomb Group.
There is no reason that Hogan would need to know the courier schedule of flights coming into England, let along that General Butler was on the flight.
There is nothing that states how the antenna got from the barracks, where Hogan turned it into a swastika, to the top of the mast on the flagpole on Klink's office.
After the new antenna extension is in place on top of the old antenna, the gang is using the radio to communicate with General Butler via Morse Code. However, the old antenna (which the extension is attached to) is not extended. Kinchloe would have extended the old antenna to raise the antenna extension to its highest possible point to get the greatest possible range, as the plane is too far away for the signal from the old antenna alone to reach the plane (thus the need for the extension).