Shades of Calvin and his bicycle here. And a scribble of ire!
A character displaying affection, love, tolerance, pleasure, joy? These things are not funny. Conan! What is funny in life?
Lucy turns into quite the feminist later on, this attitude turns out to be fairly atypical of her.
It's possible to miss it if you just glance at the strip, but the joke here is that Lucy is missing one skate, which is the one that Snoopy's riding.
Violet and her mud pies again. Old habits die hard. Y'know, I don't remember if we've ever seen any of the Peanuts kids eat one of those mud pies. I'd assume that they're just playing, but that look of distaste on Charlie Brown's face implies that he at least has considered eating one of the things. I guess kids had stronger immune systems back then.