Factual error: Jack lives in suburban Detroit, yet there are palm trees along the streets.
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.
Answer: Black armbands are a traditional sign of mourning, though not widely used today. They are wearing them to mourn for Jack.
raywest ★