Follow the Leader: The way the children featured in the live-action sequences all wear red sweaters is similar to how the hosts of This is Daniel Cook and its spinoffs all wear orange clothing.
Market-Based Title: The Canadian, British, and Australian broadcasts of the show are titled "Daniel Tiger's Neighbourhood".
Network to the Rescue: While the show remained off Netflix in the US, In Asia Netflix picked up the show a few months after Disney Junior Asia screwed the show over, making it once again available in the region.
Screwed by the Network: The show was initially picked up by Disney Junior Latin America and Disney Junior Asia, but only lasted a season on those networks, as a result of Disney refactoring their networks to focus on only in-house shows. Episodes from Season 2 onwards, which introduced Baby Margaret to the Tiger family, were not broadcast.
For "A Storm in the Neighborhood / After the Storm," the idea was floated of the storm taking out a tree where some of the characters lived, but it was decided this would just be too much for the show's target audience of preschoolers. This presumably would have been the tree that's the home of the Owl and Kittycat families, since they're the main characters who live in a tree and in the episode, they sleepover at the Tiger household to take shelter. The idea was retained only in that a tree does go down in the episode, but it's just a random tree in front of the clock factory that nobody lives in and Trolley helps to clear it away.
The writers / developers considered giving a character other than Daniel a sibling, but found in their research that anything that happens on the show tends to have more impact for the target audience if it happens to Daniel. This is also likely the reason why from this point forward pretty much anything major that happens on the show happens to Daniel.