Yes that sounds to text book ADHD I would talk to their doctor about this and get him teste . My son who is five was doing the same exact things, it actually sounded lime you were talking about my son there for a minute lo . Just a little side now when he says I forgot he's telling the truth, there so much going on in his little brain he can't comprehend a lot he's being told. For now just tell him one thing at a time, when it comes yo other things like getting ready in the morning or for bed or cleaning his room go by a check list if not he won't be able to follow or retain all of it in his little mind at one time. But yes I def think he has ADHD and needs to be tested and diagnosed officially so you guys can decide which form of treatment is best for him.
Well, the first thing to realize is that to punish him for something that he has done at school - won't work. To change behavior - you need consistent, immediate reinforcement. And the key word is immediate (well, consistent is also pretty important). You are punishing him hours after he has done something. A child of this age can't connect the two things. Only the school can deal with things that happen at school. Now once he hits about 5th grade, then actions at home will have a greater chance of success.
You need to deal with why this is happening, then you can provide the proper means to change his behavior. Since you posted on an ADHD forum, ADHD must be going through your mind. With good reason. He is showing many of the symptoms. And, if he does have ADHD, what you (and the school) are doing will only make things worse - as you are beginning to find out.
I could not tell from your post if he is having the same problems at home. That is pretty important to know. Also, if he had these problems last year. If this has only happened this year, that changes things.
While I am waiting for you go get back to me on the above questions .....This is a good starting point for finding out about ADHD. http://helpguide.org/articles/add-adhd/attention-deficit-disorder-adhd-in-children.htm
And while I have a lot of very specific resources - you might want to check out his link ...http://www.additudemag.com/resource-center/adhd-parenting-skills.html
Hope this helps, keep in touch!