Miss Nelson is too feminine to be assertive.
There's some kids in school. It's unclear how old they are because of the stylized art. They could be anywhere between five and fourteen, for all I can tell. But their class has "story hour", so they're probably younger, like first or second grade (in 1977 you didn't really assign homework to kindergartners). The children in the class are acting up. They're throwing paper planes and such, and the teacher, the titular Miss Nelson, can't get them to calm down by being nice to them, so she's frustrated. The next day they have a new teacher named Miss Viola Swamp. She's ugly (as opposed to the pretty Miss Nelson) and clearly mean. She makes them actually do what they're supposed to be doing! And doesn't even allow them to have a story hour! She's their substitute teacher for several days. They go to the police trying to find Miss Nelson because they miss her, and the police are not helpful. The kids go to Miss Nelson's house, but nobody is home, and Miss Viola Swamp is walking by, so they run away.
They're sad, because they figure Miss Nelson's never coming back, and then Miss Nelson comes back. They say, 'Where were you?' and she says, 'That's my little secret.' She notices that during story hour, no one is "rude or silly." She asks them what caused the change, and they say, 'That's our little secret.' And at the end, she goes home, and it's made pretty clear that Miss Viola Swamp was actually Miss Nelson in disguise.
Basically what it boils down to is, children don't listen to nice people. You have to threaten them in order to make them behave. Which is ridiculous. I mean, clearly you have to give them consequences for bad decisions. On the other hand, Miss Swamp doesn't seem to be that mean. She raps the desk with a ruler. She snaps at the kids. "They could see that Miss Swamp was a real witch.... She meant business. Right away, she put them to work. And she loaded them down with homework." She tells them, "Keep your mouths shut," "Sit perfectly still," and, "If you misbehave, you'll be sorry." That's it. That's like the only difference between the teachers. They just don't like that she gives them a lot of homework. She's strict, I'll give her that, but the children should be sitting still and being quiet in class, and not misbehaving. The kids basically assume that she's a horrible person because of her looks. And apparently only mean people make you learn things.
In the beginning, when the children are playing with spitballs and paper planes, giggling, squirming, making faces and being rude, and refusing to do their lessons, the only thing Miss Nelson does is say in a "sweet voice", "Now settle down." When her class is acting up, she just gives up and pretends to be some kind of nasty individual who just doesn't respect her students. Of course, they've already shown that they're not currently worthy of respect.
It took me a few minutes to realize that, really, this book is sexist. Viola Swamp, the assertive one, is portrayed as expressly ugly, a non-feminine trait. She's a "witch." She "mean[s] business." Miss Nelson, her alter ego, is pretty, blonde, passive, and talks in a "sweet voice." Miss Swamp is described as "wicked," when she's really just assertive, bordering on aggressive. You don't call an assertive male teacher a "wicked" "witch." But the reality is that Miss Nelson isn't capable of becoming more assertive until she also becomes less feminine. When a woman is assertive, they are described in disparaging terms, and people only like them if they're "nice" and "sweet."
What it boils down to is, don't have respect for people who treat you kindly. The only two opinions the children can have for the teacher are disrespect, or fear. Really, the best relationship between an adult and a child is for them to have mutual respect and understanding of the other's position. It's obviously a lot harder for children to understand the position of the adult. A really great book that deals with this in a teacher-student context is "My Teacher is a Monster! (No, I Am Not.)" by Peter Brown. It starts out with the child being a troublemaker, but he comes to act differently not by the teacher being a complete jerk to him, but by realizing that his teacher is another human being worthy of respect, and trying to get him to behave in order to teach the class, not because she's a terrible person. Children need to have reasonable consequences to their misbehavior, otherwise they don't understand why they shouldn't do things. In "Miss Nelson is Missing", the consequences don't make any sense, and the children are only punished by seeing how "it could be worse". Knowing that others have it harder doesn't make you really respect what you have.
Teaching is a difficult job, but it's important that children learn at school. There are so many things that school teaches that improve people's lives and interaction with society. And this book sends the message that nice, respectful, and feminine, are not good ways to get people to do what is helpful for them.