Factual error: Jack has it pointed out by Annette that it's only 8:30pm in California (when the kids are eager to call their mom). When the next scene shows the exterior of the hotel in California, there is still some twilight left in the sky. However it is early November (since Carolyn left for the airport on Halloween) and it's impossible to have daylight of any kind around 8:30pm at that time of year. The sky would be pitch black much earlier than that.
Audio problem: When Ron hangs up the phone in Caroline's hotel room, and she comes out and asks who was on the phone, there is an obvious echo when Ron answers 'wrong number' indicating poor acoustics from the sound stage.
Audio problem: When Jack has baby Megan hoisted over the hand dryer, Kenny calls out to him in an echo, and Jack answers in an echo, indicating a bad sound acoustic in the obvious studio space.
Answer: Black armbands are a traditional sign of mourning, though not widely used today. They are wearing them to mourn for Jack.
raywest ★