While those might all be symptoms of ADHD in an older child, they could also be a sign of an immature three year old boy. ADHD is difficult to diagnose in preschool age children.
Instead of jumping on an early diagnosis of ADHD for your son, you might consider that you have unrealistic expectations for what he should be doing at this age. Many three year olds still have short attention spans, are hyperactive and like to play, and wouldn't be expected to sit still for long periods of time.
If ADHD runs in the family, if he is also overly aggressive and it is leading to problems with his relationships with other children, or if his behavior is extreme and very different from all of the other preschoolers at his age, then you might seek further evaluation by a child psychologist or your pediatrician.
Considering a diagnosis of ADHD in a preschool age child poses some big dilemmas. While you don't usually want to start these young children on ADHD medications, you also don't want them to go several years with untreated symptoms that may lead to problems learning, making friends, and cause low self-esteem.
It is important to keep in mind that preschoolers can have ADHD, but as Dr. James A. Blackman said in his article on "ADHD In Preschoolers - Does It Exist And Should We Treat It?," 'high activity level, impulsivity, and short attention span-to a degree-are age-appropriate characteristics of normal preschool-aged children.'
As a way to assist you in coping with his behavior, you may want to read the book "Raising Your Spirited Child: A Guide for Parents Whose Child Is More Intense, Sensitive, Perceptive, Persistent, Energetic," by Mary Sheedy Kurcinka.
Recently, temperament traits have come to the forefront of child development theory. In "Raising Your Spirited Child," Mary Sheedy Kurcinka's first contribution is to redefine the "difficult child" as the "spirited" child, a child that is, as she says, MORE. Many people are leery about books that are too quick to "type" kids, but Kurcinka, a parent of a spirited child herself and a parent educator for 20 years, doesn't fall into that trap. Instead, she provides tools to understanding your own temperament as well as your child's. When you understand your temperamental matches--and your mismatches--you can better understand, work, live, socialize, and enjoy spirit in your child. By reframing challenging temperamental qualities in a positive way, and by giving readers specific tools to work with these qualities, Kurcinka has provided a book that will help all parents, especially the parents of spirited children, understand and better parent their children.
Good luck!