Visible crew/equipment: At the Officers' Club, after Potter and Tucker's practical joke is out of the bag and they're congratulated, when it cuts to everyone sitting at the bar, at the start of this shot the boom mic is visible at the top, left side of the screen just before it's pulled up.
Other mistake: When Charles, BJ and Hawkeye steal Margret's tent, what's left is a frame of wood, including roof beams. From other episodes we know that the tents are held up by a wooden frame around the edges and a center pole. We even know for a fact that Margret's tent is built that way, because in an earlier episode Hawkeye and Trapper saw through the center pole of Margret's tent. We also know that the construction principle of the tents hasn't fundamentally changed since then, because when Hawkeye finds the oatmeal in his boot earlier in the same episode, you can see the center pole of the Swamp.