I spoke too soon regarding the spelling of "coconut." Actually, it's possible this is the first time Schulz called it "cocoanut," and I misremembered. I sometimes scout ahead a few months so I know what's coming up, and I might be remembering this odd spelling from that.
Charlie Brown's distaste for coconut is one of those facts about the character that didn't really survive into the later strip.
This is the first strip in which Linus holds a blanket, and the first one in which we're told he does it for security-related purposes, although the explicit term "security blanket" isn't in use yet.
On the art of extracting comfort from flannel. Lucy isn't really opposed to it at this point -- in fact, I think you can probably find several strips in which Lucy is anti- and pro-blanket. Their grandmother, however, is less divided about it.
Snoopy keeps one part of his brain awake at all time to watch for food opportunities. It's like a processor devoted to background tasks.
We get the serif-Z representing sleep here again.
We've seen versions of this strip before. An early strip had them playing hide-and-seek, and the width of Charlie Brown's head gave him away.
In fact his head isn't that much wider than the others, it just seems to stick out more. Patty would have trouble hiding behind that tree without the sign (also because her dress extends out wider).
Snoopy vs. The Yard: The Faucet
Even assuming the dog isn't familiar with the workings of human gardening apparatus, it's an oddly specific place to choose for a nap.