During the dance scene where no one was dancing, Peppermint Patty was among the group of girls, then when Charlie Brown opened the door, she reappears along with Marcie, holding the fruit punch.
Charlie's hands get covered in ink while writing his book report. He then wipes his hands on his shirt creating the characteristic zig zag pattern. However, in all subsequent shots the pattern disappears and his shirt is again a solid color with no pattern.
When Charlie Brown goes to bed after writing his book report, while he is getting into bed we can see some notes beside his window sill. However, when Sally comes in and wakes him a few seconds later, the notes have vanished.
When the little red-haired girl's pencil falls on the floor it rolls in a straight line between the desks towards the back of the room. As it has a wider section on the end, it should roll in a curve.
Charlie Brown is forcefully towed by his kite across the frozen lake, even though there is zero wind (as shown by the gently falling snow flakes). However this is essentially in keeping with the style of how snow was drawn in the original animation and comics, and may be a deliberate choice by the filmmakers.
Snow falls during the ice skating scene at the beginning of the movie, but there's blue skies and not enough clouds in order to produce snow.
Linus is a year younger than Lucy and Charlie Brown, and would not have been in the same class as them. This is because he skipped a grade, which was not an uncommon practice when the comics were written.
The Red Baron's triplane lacks the Iron Cross symbols that the real plane had in both Linus's original model and in Snoopy's fantasy sequences. Linus may have forgotten to include the Iron Cross symbols or had not yet painted them on, while the Red Baron's plane in Snoopy's fantasies was based on the model plane because it hit him while he was trying to climb into the classroom through the window.
At one point Snoopy determines which way the wind is blowing by dropping a handful of grass. The grass is carried away by the wind, but the snowflakes fall straight down as if there is no wind.
Charlie Brown writes 1,000 words for his book report but when we see his book report it's only two pages, which is way too little to hold 1,000 words.
At the summer fair, Charlie Brown gets in the way of Violet in one of the games. She remarks with Lucy's voice.
When Charlie Brown is learning to dance using the foot markers laid down by Snoopy, he counts; "1, 2, 3, 4" but as he says "4" he puts his left foot down on the marker that says "3". Of course this is what we'd expect from Charlie Brown ...