hi jamie b - i don't know if it's "normal" or not, but it sure sounds familiar. I think i must say "watch where you're going" every single time we're out somewhere with DS5. There are just so many other things to think about that are much more interesting than watching what's ahead! It seems like this is improving a bit - i remember I used to have to pull him out of the way of carts at the grocery store a lot more. hmmm - maybe that's only better because he's been sitting in the bottom of the cart lately...
We still get a few out-of-proportion tantrums too, but these are definitely starting to go away. Usually a frustration related to not getting what he wants. We found that these were reduced with parental consistency - we didn't give in to his screams/pleas, then he knew what to expect next time.
Our DS5 also likes to run around. Sometimes he just runs up and down the length of the house and says "i need some exercise!" After running around for a bit, he's fine. Last year, when he was learning something new, he would get very excited and run around - a whole body response to the excitement of learning.
As for paying attention, i think it's very common for 4yos of all types to not pay attention. That said, it seems that sometimes DS5 is completely entranced by something (computer usually) and doesn't hear repeated questions from parents. Those times we have to get in front of his face for him to notice us. But then other times, when he seems to be not paying attention, he will hear something we didn't necessarily want him to hear and ask about it later! he definitely can pay attention to several things at once when he wants to.