Andrew Lee Potts auditioned for the part of Hatter via videotape. He learned how to ride horses and do hat tricks for the mini-series and liked to improvise his lines. This was not his first foray into Alice's Adventures in Wonderland, however. At age ten, he played the part of a crow in a production of "Alice: the Musical" at the Edinburgh Festival.
In the final scene, if you look very carefully, you can see that Hatter has his trademark hat (black, this time) in his hand.
When Hatter (Andrew Lee Potts) and Charlie the White Knight (Matt Frewer) are trying to get into the Heart Casino, Hatter says that they are Robinson and Duckworth. Robinson Duckworth was a friend of Lewis Carroll and was present in the creation of Alice's Adventures in Wonderland.
It's revealed, when Alice explains the watch, that it belonged to her father, "Robert Hamilton". Which is Lewis Carroll's father's name, Robert Hamilton Carroll.
Lewis Carroll was the pen name for Charles Lutwidge Dodgson. His father's name was Charles Dodgson, and his mother's name was Frances Dodgson.