Bandersnatch becomes kind (Situational Irony)
The Bandersnatch comes after Alice at the beginning of the film in order to kill her, and it stands out as one of the most ferocious and formidable beasts in all of Wonderland. However, after Alice returns the Bandersnatch's eyes and proves that she is not its enemy, it changes its attitude towards her and becomes her friend. Alice's act of kindness leads to this ironic twist, in which the creature that has most hurt Alice becomes the one who can help her the most.
Just a Dream (Situational Irony)
Alice believes that this whole experience in Wonderland is just a dream that she will wake up from at any moment. She pinches herself and tries to remain unfazed by the events surrounding her, until she finally remembers that Wonderland is very real. Not only that, but it is a place she often visited when she was a child.
Alice's Identity (Dramatic Irony)
When Alice first arrives at the Red Queen's castle, the big-headed queen has no idea who she is and Alice lies, telling her that her name is "Um." For the next day or so, Alice and the other members of the resistance are the only people who know Alice's actual identity, but the queen has absolutely no idea. Thus, there is a discrepancy between what the viewer knows and what the Red Queen and her courtiers know, leading to some dramatic irony.
The Queen's courtiers wear prosthetics (Dramatic Irony)
In another moment of dramatic irony in which the viewer knows something that the Red Queen does not, the Red Queen's courtier's prosthetic nose falls off during a conversation, and the Mad Hatter spots it. He realizes that the Red Queen's courtiers are only pretending to have unusually large features to gain favor with their large-headed queen, but the courtier manages to affix her fake nose to her face again before the queen sees. Thus, we the viewer again know something that the Red Queen does not.