While the N-word is a problem, the issues with the novel go deeper than a mere word. Context is everything, and critics complain that the deeper issue is the way Jim is stereotyped as a childlike person, although he is an adult. He is treated like a "boy" by the actual boy characters Huck and Tom. Jim, critics say, shows very little agency or self-assertion and is too willing to simply follow along with Huck and Tom's plans. It's as if he can't think for himself. This reinforces ugly stereotypes of black people as unintelligent and childlike and in need of white guidance and supervision to get along in the world. One could understand how this would grate and even be deeply upsetting.
Further, some have been appalled that Huck feels he is a "sinner" for helping Jim escape slavery, completely missing Twain's satire of the upside-down morality of the Old South. Twain meant his audiences to laugh at Huck for his worries; clearly he is the one person in the novel doing the decent thing by Jim. Audiences are meant to question if aspects of their own moral codes are equally twisted or senseless. It might also be noted that Twain, who deeply abhorred slavery (though writing the novel after slavery's end), like Harriet Beecher Stowe in Uncle Tom's Cabin, had to make his black characters palatable and sympathetic to largely white audiences. Clearly, there is much to recoil from and reject in the portrait of Jim; at the same time, for that very reason, the novel becomes a profoundly teachable moment--but many argue that students will take away the wrong lessons.