The children, Peter and Wendy, generally misbehave in a manner that we would expect; they act contrary to their parent's wishes when they aren't being directly observed, deflect blame, and then complain when they receive a punishment. Their key "misbehavior," if it can be called that, is the fact that they lock their parents in the nursery at the end of the story and allow them to be consumed by lions. Furthermore, this is foreshadowed throughout the story, such as when Peter and Wendy's parents hear screams and discover their personal items in the nursery, in retrospect obviously having been mauled by the lions; we are meant to understand the children used the nursery to visualize, in graphic detail, their parents being murdered, which is arguably a much more severe misbehavior than lying or whining.
The first misbehavior we can be fairly certain of is Peter manipulating the nursery so it no longer accepts commands from adults. This is not actually evident until the end of the story, although evidence for it accumulates throughout. Second, Wendy is suspected to have changed the settings of the nursery in order to deflect suspicion. Finally, the tantrum the children throw when their father finally shuts the nursery off is a remarkable reflection of the earlier statement, that the children live for the nursery; indeed, it seems to be the only thing they care about, more so than even their own parents.