Narm Charm: Some of the children providing the voices were too young to understand their lines, resulting in the classic awkward delivery that later became a staple of all Peanuts specials (the lines you hear are often a composite patched together from several different takes).
The whole "Snoopy shot down behind enemy lines" sequence. That eerie flute music (coupled with the distant gunfire and air-raid siren) doesn't help.
Not to mention the opening title sequence, which shows the kids in their costumes running around, clearly terrified, from Halloween monsters like skeletons, witches, and big black cats. They eventually hide in a pumpkin patch, but it ends with an Ominous Owl flying at the screen. The whole thing is a Disney Acid Sequence and Big-Lipped Alligator Moment, to boot.
Completely justified, of course, since this is a Halloween Special we're talking about.
The Woobie: Linus, when he is still freezing in the pumpkin patch at 4 a.m.
And, as always, Charlie Brown. Apparently this child is even deeply hated by adults, so much so that they would all give him a rock as opposed to candy.
Schroeder plays some WWI songs for Snoopy. Snoopy dances to the music, but when Schroeder plays a couple of sad songs, poor Snoopy starts crying so hard that he leaves the party. It just makes you want to give Snoopy a hug.