We should define "major conflicts" in terms of story development first, before delving into the specifics of The Misfits.
A plot conflict, despite the name, does not necessarily have to be a fight, confrontation or argument, and it definitely doesn't have to take place between two people, or even between people at all. Basically, a conflict is anything divisive, perhaps requiring that one have an opinion, or make a choice. Conflicts are not necessarily "bad" - after all, if we didn't have to make any choices or take any sides, we'd all be pretty much the same - but conflicts do tend to force characters to grow and act, whether or not they're ready for it.
One conflict, which takes place on a societal and even a biological level, is growing up. This is a pretty classic theme for "coming-of-age" style stories such as this one, in which characters are forging their identities and finding examples that inspire or repulse them (such as Bobby's desire not to be like Mr. Kellerman). Many of these conflicts are born directly from the fact that these people are seventh graders being overseen by adults; consider that there's nothing stopping an adult from creating a Freedom Party if they wish to, but Addie has to ask permission. Many of these conflicts are born from the children attempting to express themselves in more adult-like and individualized ways, but being restrained by adults and their peers for a variety of reasons.
Another, more specific conflict, is the one between Bobby and Mr. Kellerman. This is, in a way, another facet of the "growing up" conflict; for example, much of Mr. Kellerman's dislike of Bobby stems merely from Bobby's age. Later, when we learn that Kellerman is a lonely and lost person who "doesn't know who to listen to anymore", it seems that it is in fact Kellerman who is the child; he failed to develop an independent identity, and his anger is really just frustration at being trapped in a sort of eternal childhood. On a more day-to-day level, though, we could identify this as a conflict between Kellerman's bad mood and Bobby's need to keep his job.
The first conflict is more of a general theme for the book, and the second is a specific interaction between two characters. The third conflict I've chosen is a conflict between ideas; specifically, it is Joe's feminine behaviors. Joe wore dresses when he was young, and in seventh grade he paints one of his nails and dyes his hair; this and other behaviors inspires some students to call him a faggot. While the name-calling is itself a conflict, it is born from a deeper and broader conflict; a conflict between what society establishes as "male appearance and behavior" and what Joe is doing. People are unhappy with Joe because he has chosen to visibly and blatantly reject the behaviors that society has deemed appropriate for him, and so he is being "punished" for it with the name-calling. This is slightly different from the standard "growing up" conflicts, because the person Joe is growing up to be is fundamentally an outcast.