PERSONALITY
At the very start we learn that Alice is insecure about herself, and quite jealous of her sister. She is very practical and cynical of things, and especially doubtful that Wonderland is a world she wished for, but remains strong compared to most leading ladies of the Alice in Wonderland tales. She often follows her beliefs and is determined to find her way home once through the rabbit hole. She stands up for herself and others that seem weaker, even standing in front of Peter's gun so that he won't kill a random messenger with no face. Her want to help others is proved when she tries to save a stranger from the Afterimages, and is upset when she realizes that she can't move.
On the other hand, Alice also has her aggressive side. On several occasions, Alice resorts to physical violence if she's irked enough. Peter is often on the receiving end of her fist, and even Boris gets his tail pulled and his foot stepped on when he upsets her. There are no bounds, as the great Mafia leader Blood Dupre also becomes the target of her frustration when she throws a hard cover book directly at his head. This goes to show that Alice is hardly the completely passive type, despite her dislike for guns and the weight that comes with them.
I believe Alice's greatest strength is her ability to say what's on her mind, and to be honest with her friends and others around her so long as it doesn't concern her own personal problems. She even argues with Blood that he looks angry, despite knowing that he's the Mafia boss and could at any moment order the others, sans Boris, at the tea party to kill her. I think it's fair to say that Alice expects the same from her friends, and prefers a painful truth to a sugarcoated lie.
Her greatest weakness, unfortunately, is toward anything that's remotely cute. Even though she tells Peter she will never like him, as soon as he changes into his rabbit form she can't resist and tends to go along with whatever he asks of her so long as he remains cute. Even Elliot cannot escape her, and after she's comfortable being around him she grabs his ears regardless of his cries (she later apologizes, of course).
The other most apparent weakness of hers is concerning her feelings toward her sister. While it's obvious that she admires and loves her sister, Alice can't help but constantly compare herself to her (and other ladies that come into her life as well, such as Vivaldi) in looks, manners, personality, etc. She thinks less of herself next to another, and it tends to warp her belief in what others might say or think about her.
Aside from the emotional and mental weaknesses, after arriving in Wonderland Alice began to slowly suffer from a third weakness; any thoughts of home, especially concerning her sister, began to hurt Alice. It could start with a headache and something of a chest pain would continue until she was soothed of her own thoughts, then she recovers just as quickly as it begins with no recollection of what she had been thinking about beforehand.