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.
Not a coincidence, though — Tommy Wiseau admired James Dean and put the line in his movie as an homage to this one (though amusingly, he initially got it wrong and had to be corrected by the rest of the crew).
Ho Yay Shipping: Jim and Plato. Of course, considering that James Dean was rumoured to be bisexual, director Nicholas Ray was definitely a bisexual and that Sal Mineo was gay, it's more than just subtext.
Foe Yay: The legendary exchange between Buzz and Jim:
Narm: Averted. Jim's cry of "You're tearing me apart!" is more effective than you would think—even after seeing The Room. James Dean being an astronomically better actor than Tommy Wiseau undoubtedly helps.
Though there is a straight example with the poor dubbing of Plato's line "I have to go warn him!"
Seinfeld Is Unfunny: This film made or codified several tropes that went on to be mainstays of the way teen angst would be depicted for the next 50 years. For example, elements of several early episodes of The O.C. are explicitly drawn from parts of this movie. As a result, much of it seems cliché today; when it was released, it shocked audiences.
It should also be noted that the film is not about "rebelling" as such but having "nothing" to rebel against, in that the cast are spoiled rich kids with everything provided for them but not really content and seeking a deeper purpose and a community and culture of their own. This was a huge subversion of the juvenile delinquent theme which believed Society Is to Blame. The point is that post-war prosperity will not alone guarantee safety and comfort.
Also the first film which showed teenagers living and forming a counter-culture which heralded the 60s in a big way.
Unintentionally Unsympathetic: Sympathizing with a guy with Jim's problems, okay. Sympathizing with a guy who kills puppies, on the other hand...
Values Dissonance: At one point Jim realizes he's so screwed up because his dad never beat his mom.
Jim thinks his father is weak because he seems to do a lot of the cooking and cleaning in the house, and Jim believes that cleaning up is women's work. Today, any man that doesn't at least clean up after himself is likely to find himself divorced and out on his ass.