Alice always has at least one item of blue clothing on at all times during the movie. As her mental state starts to deteriorate, the shade of blue becomes progressively darker.
The Mad Hatter's dream world costume is inspired by Heath Ledger's Joker, Gary Oldman's Dracula and Nosferatu. It combines the Victorian look of the Dracula costume with the purple and green of Joker's, whilst also having a cushion built into the upper back/shoulders of the jacket to provide the hunch back style look of the Vampyre. Actor Jon Campling called the costume the best he had worn since his Death Eater one in Harry Potter and the Deathly Hallows: Part 1 (2010).
The radio that can be heard in Alice's bedroom is announced as Radio Cheshire, a play on the Cheshire Cat. We first hear from it with the sports reporter rounding up his report on AFC Wimbledon's historic victory, the club supported by writer/director Jake Sleet. Funnily enough, AFC Wimbledon were promoted in the play-offs to League 2 a couple of months after said scene was written.
The main Alice was originally going to be English and visiting her grandparents for the weekend. She was going to be an employee of Lidl supermarkets, which would have seen her wearing a blue jumper with a name-tag showing her first name with Lidl underneath, a play on Alice Liddell. However, when Lidl wouldn't give permission to use their store, and American 'Shea Hall' won her audition, the decision was made to make Alice an American visiting her English grandparents for the Summer.