These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Dysfunction Junction: Larry's family seems like a bit of a mess. Anytime he even mentions his family, he talks about "getting hollered at", and they openly say that his father hits him and his sister. His father seems to travel frequently and every time he's out of town, his mother acts like a basket case. There are also mentions of her getting nervous headaches when her children misbehave AND when they get disciplined. It's treated as a joke but the longer you watch the sorrier you feel for Larry. He's not a very bright kid but his home sounds like an unpleasant place, which may explain why he spends so much time at Beaver's house (something Wally comments on fairly often, 'gee, with the number of meals he's eaten here...' etc)
Indeed, Tony Dow ended up becoming so popular, that in the later seasons, the writers started writing episodes in which Wally would get into the schemes and scrapes that Beaver would usually get into, with Beaver becoming more of an observational character.
And, of course, Eddie Haskell
Not to mention Clarence "Lumpy" Rutherford, bad girl Judy Hensler and even Gilbert Bates.
Hilarious in Hindsight: In one episode everyone was aghast that Beaver was actually selling water to people! Mind you, it wasn't so much that he took advantage of inside knowledge that the water main would be shut off or that he was selling it out of a bucket on his wagon, but mearly the fact that one person could be low enough to sell water to another person! How Evian spelled backwards of them!