The problem with really intelligent kids is that they problem solve so fast. And the problem with 4 year olds is that they don't have alot of self control. Put it together and ya - you've got problems. Throw the possibility of ADHD into the mix and everything gets a lot worse. I really don't know if he has ADHD. How long ago did the doctors see him and what kind of a doctor saw him? The reason I ask is that In October 2011, the American Academy of Pediatrics (AAP) released new clinical practice guidelines for the diagnosis, evaluation, and treatment of ADHD. It now does cover 4 year olds. However, "For preschool-aged children, evidence-based behavioral therapy alone is recommended as the first step toward treating ADHD symptoms and associated impairment." So even if meds are not given - the therapy is recommended. They can not just ignore the situation and say come back later on.
You can read about it here. http://www.medscape.com/viewarticle/759086?src=nl_topic
If you do want to check out the ADHD aspect - this site has a pretty good list of things to look out for. http://www.rxlist.com/attention_deficit_hyperactivity_disorder_adhd/article.htm#tocb
And, of course, its possible he does not have ADHD but is an overactive, intelligent 4 year old. Many of his actions are not that extreme. I suggest you read all of this post from the child behavior forum from someone with kind of similar problems. There are a lot of good suggestions of ways to help, and I think that many would be helpful for you.
The link is http://www.medhelp.org/posts/Child-Behavior/6-year-olds-behavior/show/1714289#post_7850204
Hopefully, some of this helps. Please post if you have any more specific questions about ADHD. You also might want to try posting on the child behavior forum for other ideas on working with your child.