These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
It does foreshadow the fact that Alice's father is in Wonderland, though it's more for the audience's benefit than any of the characters'.
Most of the scene where Alice is trapped in the copy of her house by the Tweedles would count. This includes a part where she turns into a younger version of herself and fearfully walks into a room to find a pig in a bonnet in a crib. Of course, the people who made the series used this all as an opportunity to shove a ton of references to the book in.
Crazy Awesome: Charlie, especially during the skeletal army scene.
Fanon: The technicians who work under Carpenter and Walrus are normally referred to as Eggmen.
And Lady Gaga is secretly from this version of Wonderland.
Friendly Fandoms: Considering these are the same guys who whipped up Tin Man, the fandoms share a lot of writers and discussion boards.
There's also a lot of crossover with Primeval.
Genius Bonus: The White Knight, when meeting Alice and Hatter for the first time, says, "My nana used to say that if I was the only eligable batchelor left in the world, there wasn't a warthog or wall flower who'd polish my escutcheon." An escutcheon is a type of shield, but it is also used in medicine to refer to something else.
Memetic Mutation / Iconic Outfit: Oh, so many. The playing card suit worn by those attached to the Casino indicates their function in Wonderland:
Diamonds: Dealers, dancers, scientists, technicians and anyone else dealing directly with Oysters.
Clubs: Bureaucrats and pages.
Spades: Security force; the strongest members are referred to as "Aces" despite being all Spades of various high-end numbers.