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.
Award Snub: Probably the Most Egregious Example. It won absolutely nothing.
Bittersweet Ending: Brooks and Tommy are dead. Andy wasn't exonerated, and Blatch still got away with his crimes. Red is violating his parole by going to Mexico to meet Andy outside of jail, and they are probably both on the run from the law and in no position to turn to it should anything happen. However, Norton did get exposed as a crook, and ended up shooting himself; Hadley got arrested for his role in the murder of Tommy; and at the very end of the movie, Andy and Red finally get to enjoy their friendship outside of jail, which surely must be refreshing for them. It is for the audience.
On the other hand, Brooks was an old man at the end of his life, and chose to end it with what he saw as dignity. Tommy's death is sad, but his killers pay for it. Blatch seems the sort to have met a bad end at some point, so we can hope. And Mexican authorities generally don't care too much about people who are wanted in America unless they get on the Mexican authorities' nerves, and even then will look the other way for a handful of cash, which Andy has plenty of. They'll both be fine. Still bittersweet, but it's more sweet than bitter.
Red and Brooks, as lovely as they are, did something to warrant their life sentences in prison. Red, we know, committed murder, and it's quite likely Brooks did, too. Andy, while he didn't actually kill anyone, did seem to consider it, seeing as he stalked his wife with a loaded gun while drunk.
Ear Worm: The music that plays when the police are coming to get Captain Hadley and Warden Norton.
Family Unfriendly Aesop: The storyline implies that it is justifiable to unlawfully escape from prison in a society that thinks you are a murderer, if you were wrongfully convicted. It also implies that it is justifiable to engage in all kinds of sneaky treachery, including setting up a complex scheme to launder money for one person, so long as you plan on using that same scheme to expose the person you were laundering money for as a crook. In other words, this movie implies that ends justify means. Yes, it has family-friendly aesops as well (the themes of hope and perseverance come to mind), but the moral perspective implied from some aspects of the movie (especially the scheming, underhanded nature of the protagonist) is quite at odds with more conventional forms of morality.
Fandom Rivalry: In 2008, a somewhat complicated series of votes on the Internet Movie Database to give The Dark Knight the spot on the Top 250 as the #1 film of all time (that was from The Godfather) ultimately led to Shawshank topping the list. The Godfather had held that position for quite a long stretch of time, and its fans were, to put it mildly, not impressed; even now, over a year later, a visit to Shawshank's IMDB forums reveals thread after thread attacking it as unworthy of being #1 (and, implicitly or explicitly, favouring The Godfather).
Hilarious in Hindsight: When Andy is describing his fantasies of Zihuatenejo, Red tells him to ignore them, describing them as "shitty pipe dreams." Andy escapes to his dreams by crawling through a shitty pipe.
Kick the Dog: The Warden clearly hindering Andy's appeal for Tommy to testify, and out of the blue ordered him to serve a month in solitary confinement.
Heywood did this earlier in the movie, as he taunted an emotionally-overwhelmed prisoner by reeling him in with what starts out sounding reassuring, only to go on to something that is practically the opposite of reassuring.
That emotionally-overwhelmed prisoner then broke down in tears, and Heywood laughed at this out loud. For what it's worth, Heywood actually turns out NOT to be a Complete Monster (which shows when we see him wanting the prisoner he taunted to shut up from crying once Hadley comes in the room), but given what he did, who could blame viewers for expecting him to be?
Memetic Mutation: The scene where Andy plays opera music for the prison has been edited many times on Youtube. Said opera music has been replaced by various kinds of music, from pop music to heavy metal, and even by flea market ads. To be fair, the reactions of the prisoners and the warden made it pretty ripe for parody.
Moral Event Horizon: The Warden ordering the death of a recently transferred con (Tommy) who has evidence of Andy's innocence, so that Andy will be forced to continue working at the prison.
Also, Hadley crossed this when he threatened to throw Andy off the roof and pretend Andy fell off.Beating up the emotionally-overwhelmed inmate earlier on could be excused by claiming he did it to deter other prisoners from making noise, but his later threat has no excuse.
Rewatch Bonus: The surprise inspection scene. The tension. We weren't aware of Andy's digging-a-tunnel project by then. When the warden talks about the poster and almost forgot to return Andy's bible...
Andy: "I suppose it wouldn't help if I told them I wasn't homosexual."
Red: "Neither are they. Gotta be human first. They don't qualify."
Vindicated by Cable: And how. Ted Turner loved this movie so much, he made sure it was playing on at least one of his cable networks every weekend for about a decade, thus rescuing it from obscurity. You can still find it on TBS or a similar channel, even 15 years later.
The Woobie: Andy Dufresne himself, of course, given what he goes through, and the point that he did not commit the double-murder he is in jail for.
Don't forget Tommy. Poor kid works his ass off to make something of himself and is more than eager to help Andy. Then he gets murdered by Hadley.
Xanatos Roulette: An embarrassingly large passage in the novella just consists of Red enumerating all of the things that might have gone wrong with Andy's plan, but somehow did not. The movie, to its credit, at least tries to explain some of these problems (such as where Andy hid the rock hammer, or how he secured a change of clothes).