These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Complete Monster: Simon Legree is a chilling reminder of the evils of slavery in human form. Legree is brutal to his slaves, working them to death because he considers it a financial boon to himself. It's also made clear he'd do it solely for for fun. Legree endeavors to break their spirits and make them despair as he breaks their bodies and minds. Legree is a torturer, rapist and murderer whose only frustration is the good-hearted slave Tom will simply refuse to break, spurring Legree on to greater cruelties to force his submission.
Cowboy Bebop at His Computer: The term "Uncle Tom" comes from the minstrel show version, written by people who had nostalgia for the slave trade. This has led many to assume the book is an apologia for slavery.
Funny Moments: Yes, there's one of these in the whole drama. More exactly, the extremely sly and tricky antics that the Shelby slaves use to delay the slave trader who purchased Harry and Tom so they can help Eliza run away with little Harry.
The phrase "sold down the river" is a metaphor for betrayal in modern American English, but most modern Americans don't know its origin.
The term was also used before the book; in fact, the modern map of Washington, D.C. (the part south of the Potomac being cut off) comes from when Washington abolished slavery, and those districts seceded. Today, the old slave market is now a farmer's market. Since going down the river was to an area which, if nothing else, made it more difficult to leave the United States, yeah.
Another common idiom that came from the book: as noted in That Other Wiki, the minor character Topsy "professes ignorance of both God and a mother, saying 'I s'pect I growed. Don't think nobody never made me.'" The phrase "grew like Topsy" is still sometimes used as a synonym for rapid or unplanned growth.
Purity Sue: Eva and Uncle Tom are this. Not surprisingly, they are also the least popular characters.
This is probably Values Dissonance, as Eva was easily the most popular character when it was first published due to representing what families openly wanted from little girls: a cute and kind Proper Lady... leading to an explosion of young girls named Eva in the northern states. Uncle Tom was also popular as a character, considering the popularity of Uncle Tom plays up until past the turn of the century, although racism tended to heavily color his depictions.
Values Dissonance: Aside from the obvious racial issues; there is one point where we're recounted the story of a pair of boys stoning a kitten to death, their mother gets upset, but they never stone a kitten to death again, so lesson learned. It's treated as a case of "boys with be boys", quite at odds with today where a woman putting a cat in a bin was treated with world-wide rage.