Continuity mistake: In the beginning of the episode, watch closely when the SWAT team member opens the bunker and reaches down. His gun is between his legs and the end of the barrel is touching the ground. In the very next shot, he's suddenly holding it much higher, and it's on his left side.
Continuity mistake: When the "Mole Women" are being interviewed on the "Today Show", watch the white circular table in front of them and the couch they are sitting on. The host has a small smattering of papers and a pair of glasses sitting besides him at the beginning of the scene. Throughout the scene, he will sometimes be holding the glasses and using them to gesture, sometimes not. And the papers move about from the couch, to the table, to another position on the table, etc. True, there are several shots where they are not visible, but it would make no logical sense for him to repeatedly pick up and move them between every shot where they're visible for no reason, and he is sitting in the exact same position in every shot, with his body language showing no movement towards them. They obviously shot the scene a few different times and he placed them down in different positions each time, and the scene was constructed with these different shots.
Plot hole: The plot hinges on Kimmy finding evidence against Pastor Wayne inside of the bunker, which she ends up doing. But there's absolutely no way the police didn't thoroughly comb the bunker for evidence after discovering it. In fact, it looks like it's barely been touched in the several months that have passed. Yes, the show has a sort-of whimsical "cartoon" logic... But even in that way, it makes no sense whatsoever.