Dennis (Jay North) and his Mom lived just down the street from my Aunt and Uncle in California when I went to Jr. High (now called Middle School, I guess) in LaCrescenta in the late 1960's (January 1967 to June 1969). I only spoke with him a few times because he wasn't around much.  He was always very nice to me and I really didn't realize who he was at the time because I grew up in a very small town and we had 1 tv station - and it didn't ever have Dennis the Menace!

Dennis, while on the set of the show, was "in the custody of" his Aunt and Uncle who were, by all accounts, quite mean to him.  His mother had to work and that's why they were in charge of him.  I don't know about his father - guess he was an absentee father or something.

I remember a lot of the stuff they talk about here in this article, tho:
http://metv.com/lists/12-fascinating-facts-about-dennis-the-menace

These videos are short and worth seeing (him as an adult in 1991 and him as an older person at a Dennis the Menace reunion).  Each vid is about 3 minutes or a bit more.

This first one is sad.  The reunion ones are pretty good tho.

https://www.youtube.com/watch?v=lfFZSe__Ua0

Part 1 of 3: https://www.youtube.com/watch?v=5VX-SpA6r_A
Part 2 of 3: https://www.youtube.com/watch?v=sD2P8RCgK8g
Part 3 of 3: https://www.youtube.com/watch?v=79Y6qAK4hrg