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.
How much did Jenny hate herself due to her horrible childhood, and how much was she using Forrest? Was Lt. Dan a Death Seeker prior or just unable to cope with his loss, and how much does he manipulate Forrest? And Forrest, is he really that low an IQ or merely severely autistic? The book is notable as putting him as an Idiot Savant, what most would call a very high IQ, but extreme autism, explaining his seemingly folksy wisdom as sheer cunning.
Forrest definitely gets an alternative character interpretation from the book to the movie. The movie emphasizes Forrest's naivete and simplicity to make him a gentle, sweet soul that touches others' lives for the better. The Forrest from the book was an idiot savant, true enough, but was otherwise pretty much an angry, rather violent redneck bungling his way through history.
In fact the entire world gets this. The movie obviously features Forrest moving through a world near-identical to ours save for his presence in it, while the book features a Crapsack World that's more fitting to The Simpsons than reality.
The original music piece that plays when Forrest runs for the first time is still one of the most popular pieces to play during triumphant sections of awards ceremonies, and has been a staple of the Oscars pretty much since the movie came out.
Alan Silvestri's entire score (getting him his only Oscar nomination to date) qualifies. How much so? In spite of the movie's classic-radio friendly song soundtrack, it's Silvestri's "Suite From Forrest Gump" that gets played over the closing credits.
Crazy Awesome: Lt Dan. Never mind that he went to Vietnam fully expecting not to return alive, he gets caught in a violent storm and insults God, challenging him to destroy him. With the completely maniacal laughter he lets out, You know this man is absolutely insane and You can only love him for it.
"Funny Aneurysm" Moment: The scene where Forrest Gump helps one of the black college students with a book (while remaining oblivious to the controversy that ensues) becomes a bit weird after the fiasco where Gump's actor, Tom Hanks, gets a bit of negative publicity regarding an incident where he acts along with a black-face comedian in a comedy act.
Gratuitous Special Effects: The CGI removal of Lt. Dan's legs or inserting Forrest into live footage serve very practical purposes but the feather Book Ends are examples of this trope.
Harsher in Hindsight: Lt. Dan tells his men to change their socks regularly, and always look after their feet.
Lieutenant Dan tells Forrest that the day Forrest works on a shrimp boat is the day he'd be an astronaut. While this is a reference to the book where Forrest does become an astronaut, Gary Sinise and Tom Hanks would later star together as astronauts in Apollo 13.
It's also worth noting that during Forrest's and Jenny's wedding, Lt. Dan shows up with artificial legs he says were made from the same alloy they used in the space shuttle.
One of the historical figures Forrest encounters is Governor George Wallace at the University of Alabama. A few years later, Gary Sinise, who played Lt. Dan, starred as Wallace in a TV biopic.
Jerkass Woobie: A lot of people hate Jenny, and not necessarily for bad reasons. But it's still hard not to feel sorry for her when the film showcases her more vulnerable side.
Lt. Dan too.
Love It or Hate It: For such a movie that is really popular with audiences, it is still very polarizing. People who don't like this movie don't just dislike it, they honestly kind of hate it. Just look at the critical reviews on Rotten Tomatoes. The negative ones are truly scathing. Not to mention it beat out Pulp Fiction and The Shawshank Redemption for Best Picture at the Oscars that year.
See also its UK release - judging from some reviewers you'd think Zemeckis and Hanks had killed and eaten their families and made them watch...
Memetic Mutation: It's like a box of chocolates. You never know what you're gonna get.
Moment of Awesome: Forrest carries Bubba (and the rest of his unit before that) out of a hostile area while napalm explodes behind him (and he gets a bullet in the but-tocks for his trouble.) He earns the Congressional Medal of Honor as a result (and a Purple Heart for taking one in the butt-tocks).
We're forgetting the scene where Forrest runs for the first time?
And for that matter, deciding on a whim to just start running, and not stopping for three years.
Unfortunate Implications: Jenny's near-endlessly miserable life, as well as the general Dumb Is Good theme, makes the film a Reactionary Fantasy of sorts that encourages people to go with the flow and do as they're told instead of trying to seize their own destinies and change the system, as she tried to.