He had a tendency to lash out at his mother. At one point, he scratched his mother so hard, she bled. He also said mean things about his sister. For example, he was saying that he wished his sister was dead. Also, his relationship with his dad was strained.
In a local news article about the Dostals' appearance on Supernanny, Brenda reveals that Zachary was diagnosed with ADHD shortly after filming.
He was 5 years old at the time, he is now 15 years old in 2017.