Did Vader already know that his son is still alive and none other than Luke Skywalker since the beginning of the movie, or did he not know about it until the Emperor informed him? In the 2004 Special Edition, his only reaction when the Emperor told him, "I have no doubt that this boy is the offspring of Anakin Skywalker", is an approximately-one-second pause followed with "How is that possible?"note These lines didn't exist in the older versions. That smacks of Double Meaning; either: a) He didn't know and was genuinely surprised when the Emperor told him that his son is alive, or b) He knew that his son is alive and attempted to hide it from the Emperor because he planned to overthrow the Emperor if he managed to convince Luke to join him, and was worried upon learning that the Emperor already knew. Since Star Wars: Darth Vader reveals he knew from Boba Fett that their enemy is named Skywalker (whom Vader silently identified as his own son), it's probably the latter.
A common fan theory is that Admiral Ozzel was a double agent or rebel sympathizer, and so his seeming incompetence (not wanting to search the Hoth system, alerting the rebels' to the imperial fleet's presence by coming out of light speed close to the solar system) was actually his attempt at undermining the empire's efforts to find them. A few POV scenes of Ozzel in Legends render this unlikely in that timeline, as he is portrayed as having disdain for the Rebels and being primarily concerned with his own advancement, but it's still possible in Disney canon.
Award Snub: Many feel that Frank Oz's portrayal of Yoda was very underlooked, between his voice acting and puppeteering work. George Lucas attempted to campaign for him to get a Best Supporting Actor nomination at the Academy Awards, but the voters ultimately felt that it didn't qualify as a "real" performance.
Yoda's theme playing as he raises the X-wing out of the swamp.
The suspenseful music that plays as Luke sneaks through Cloud City isn't awesome in the usual sense, but is very effective.
Continuity Lockout: While the opening crawl does explain the general events of what's going on and it's not too hard to follow the plot, this film does have a few plot points that would confuse newcomers who didn't watch A New Hope, such as the context of why Obi-Wan appears to Luke as a ghost and Luke's initial training with him, and why Han leaving the rebellion to pay off his debt is such a problem with Leia.
Designated Villain: Everyone (notably Han, Chewie, and Leia) treats Lando like a selfish coward for selling out his friends (who were soldiers), ignoring the fact that he had a city of millions of civilians to protect. If anything Lando's willingness to chose his duty to protect his people over his friends proves he's officially put his old ways behind him and grown to take his responsibility seriously. Might even be why he got a promotion to general in the next movie.
Director Displacement: As noted on the main page, George Lucas was the executive producer, and neither directed nor wrote the final script for the film. Some fans like to point that, arguably, the best Star Wars film had the least input from Lucas, an impression which revived after the announcement of The Force Awakens. This neglects the fact that Lucas was solely responsible for the central twist of the film, which he wrote, after rewriting the first draft.
Boba Fett. He had no more than four lines in the entire series and to this day is highly regarded as one of the most popular characters in the entire series, due to his mysterious nature, and his fearlessness even in the face of Vader (and, of course, his awesome armor).
Admiral Piett. Originally a one-off character, he was brought back for Jedi thanks to fan requests.
Kenneth Colley: "My character was not originally in Jedi. But George Lucas said, 'Ken, I've got a whole bunch of letters from people wanting to know more about Admiral Piett, and I want to put him in the movie. I have no idea what you're going to do but will you do it?"
The pilots of Echo Squadron have become quite popular in the EU, especially Wes Jansen and Derek 'Hobbie' Klivian. Not to mention Wedge Antilles, who was already an Ensemble Darkhorse from the first film.
The other bounty hunters qualify, too. At least Fett was in more than one scene; Dengar, Bossk, IG-88, 4-LOM, and Zuckuss just stand around looking cool on the bridge of the Executor and nothing else. This was all it took to get them all extensive backstories in the Expanded Universe.
Captain Needa, appearing in all of two scenes (and alive only in the first), won a lot of admiration for going to Vader in-person and taking full blame for losing the Falcon. It was clear that he knew he was going to his death, but he went anyway to protect his crew.
Epileptic Trees: Between the release of this film and Jedi, there was a lot of arguing from fans over whether Vader had lied about being Luke's father (one of the proponents of this was none other than James Earl Jones). Lucas included the scene of Yoda confirming it in the next film specifically to kill any doubt.
"Funny Aneurysm" Moment: Before the asteroid chase, Han is trying to repair the Millennium Falcon when his toolbox falls on top of him, hurting him in the process. In June 2014, Harrison Ford got injured during filming for Episode VII when a hydraulic door from the Falcon set fell on top of him.
Not only that, but as she's being pulled away by the Imperials, she screams once more, "It's a traaaaaaaap!!!!"
In Return of the Jedi Leia says "I know. Somehow I've always known." when Luke tells her that she's his sister. So, about that kiss on Hoth, Leia...
The scene where R2 and Yoda fight over Luke's lamp was made even funnier when the prequels revealed that ESB was not the first time Yoda and R2 had met. It's somewhat comical to think that R2 probably realises that he's dealing with one of the most powerful beings ever to have lived... and decides to continue trolling him anyways, though it's possible that, knowing who Yoda is, he figures Yoda knows what he's doing by not revealing himself to Luke, and is just playing along by pretending to fight with him.
Han's "I know" to Leia's "I love you" was improvised by Harrison Ford, as he felt Han's scripted line "I love you too" was out of character. In Working Girl, Ford is the one who says "I love you," to which his love interest replies "I love you too."
Han's kissing Leia before being frozen in carbonite, while Darth Vader is present in the same room, is funnier after Leia is revealed to be Luke's long-lost sister and, therefore, Darth Vader's daughter. This means Han kissed Leia in front of her dad!
Luke being missing at the beginning of the movie, especially the "Nobody knows where he is!" exchange between Han and C-3PO, became this after Luke became Sir Not-Appearing-in-This-Trailer for The Force Awakens and "#WhereIsLuke" started trending on Twitter as a result. He is even missing in the movie itself and most of the plot revolves around finding him.
Since Revenge of the Sith shows only C-3PO got his memory erased, then this means R2-D2 knows Luke and Leia are siblings. It's not hard to imagine if he might have astromech equivalent of feeling Squicked out inside him upon seeing Luke and Leia kissed, but had to keep himself quiet, either to maintain the masquerade or possibly he's programmed by Bail Organa not to tell anyone about it.
The callsign of the pilot that retrieves Han and Luke from the Hoth wilderness is Rogue Two.
When he arrives on Dagobah in search of the wise Jedi master Yoda, Luke encounters a small green muppet who speaks in a funny manner. The film is clearly written with the intention of this muppet's identity reveal being a big surprise to first-time viewers... except that, since the film's release, everybody knows who Yoda is, including any new viewers who watch the films in numerical order, rather than release date order.
Magnum Opus Dissonance: A lot of Star Wars fans consider this to be the best film in the entire saga, but Lucas actually considers it the worst. Yes, that's right, the worst of all six movies.
Luke, I am your father!note Vader: "Obi-Wan never told you what happened to your father." / Luke: "He told me enough! He told me YOU killed him!" / Vader: "No, I am your father."
"Thats not true, that's impossible!"
"Search your feelings. You know it to be true!"
"I love you."
Never tell me the odds!
"Why you stuck up, half-witted, scruffy-looking NERFHERDER!"
"Luke, don't! It's a trap!"note Yep, Leia said it 3 years before Ackbar did.
"You said they'd be left at the city under my supervision!"
"I am altering the deal. Pray I do not alter it any further."
"Obi-Wan has taught you well."
Lando had no choice.Explanation Lando was given a Sadistic Choice by Darth Vader: cooperate with the Empire or have his city destroyed and people killed, so understandably he had no choice but to comply to protect his city and people. Later, he muttered "I had no choice" once when he revealed he sold them out and once when he decided to double-cross the Empire and help Leia, Chewie, and C-3PO escape. In the latter's case, Leia mocked him while he's strangled by very angry Chewie, "Oh, of course we understand, don't we, Chewie? He had no choice."
In a meta sense, it is now common for parents to record showing their young kids the big scene and uploading their reactions to YouTube.
"So long, Princess."note Han Solo's goodbye to Leia before he attempts to leave to payoff Jabba the Hutt became a common tribute to Carrie Fisher after her death in 2016.
Lando betraying Han. note Darth Vader beat Han to the punch of arriving to Cloud City. Lando was left with a Sadistic Choice of either selling out Han or allowing Cloud City and all of its inhabitants to be destroyed.
Its Atari 2600 game, which was not only pretty complex for a 2600 game, but also is considered one of the best licensed games on the system. Then fast forward to the mid-1990s and the Super Star Wars trilogy games.
The arcade game, made using the same graphics and the same engine as the previous Star Wars game.
C-3PO reached the level of scrappiness in this movie due to him gaining characterization by being a shrill worrywart that never shuts up and constantly rattles off unfavorable statistics about their current situation. He also can't keep himself from complaining to Chewie and R2-D2 when they repaired his dismantled body. However he is remembered much more fondly ever since the prequels introduced a certain Gungan.
Admiral Ozzel is an In-Universe example of this, with the novelizations establishing that the man was notorious for being shortsighted and not thinking through his strategies like his fatal maneuver at Hoth.
Seinfeld Is Unfunny: The infamous scene really doesn't have the same level of suspense on later generations as it did at the time of its release, largely due to Memetic Mutation. Not having to wait three years to find out if it's true also helps.
Squick: After Return of the Jedi, Leia kissing Luke on the mouth became this. Even though she states in Jedi that "somehow" she had "always known" that she was Luke's sister, she may or may not have done it to make Han jealous (in which case, that may or may not be an implied Retcon).
Shocking Swerve: At the time, Darth Vader telling Luke that he was his father. It came right out of nowhere and the foreshadowing from the previous movie could have referred to a different kind of father. It worked, nonetheless.
Largely on the planet Hoth due to technical limitations:
The Tauntaun shots have not aged well. The life-size puppets are fairly convincing, but the shots of them running are recognizably stop-motion.
The Wampa was mostly removed because of it in the original version. The Special Edition inserts newly filmed scenes of it.
During the AT-AT battle, the Snowspeeders (and related shots, as per Word of God) were not printed at their full opacity. This is evident in a view from the cockpit. Like the Wampa example, this was eventually fixed.
While it's easy to miss at first due to how fast it goes by, close examination of the part where Vader cuts off Luke's hand reveals that the blade completely misses his arm!
Luke goes a bit transparent when he falls down the Cloud City shaft.
When the Mynocks start swarming after Leia and Han, you can clearly see they're large sheets of plastic tied around poles because the head is completely absent from them, unlike the previous shots of them. Even Irvin Kirshner admitted that the reason they cut away from the Mynocks so quickly was because of how awful the props looked.
Suspiciously Similar Song: The Imperial March sounds a great deal like Prokofiev's "Montagues and Capulets". Not coincidentally, the two songs are juxtaposed on Epica's album The Classical Conspiracy.
In the George Lucas Altered Version, Boba Fett's voice is probably the biggest point of contention; while Temuera Morrison gives a decent performance, many people grew attached to Jason Wingreen's original voice acting as the character. However, fans find this to be a minor gripe compared to what the other two original trilogy movies have to put up with.
The 1997 Special Edition has Luke scream (for some bizarre reason dubbed in with a clip of Palpatine screaming from the following film) as he falls through the central shaft of Cloud City, which made it seem less like he was nobly choosing possible death over joining Vader, and more like he'd suddenly realised he'd have been better off joining Vader after all. Lucas himself evidently came to regret this choice, as the 2004 DVD release onwards has Luke falling silently again.
Mostly averted, however, with replacing the original Emperor hologram with Ian McDiarmid, as not only does this maintain tighter continuity, but McDiarmid simply is Emperor Palpatine to many, and his performance is seen as much better than the rather monotone voice-over Clive Revill provided in the original version. The fans who complain about this change are actually in the minority. However, some added dialogue for Palpatine and Vader did add a new meaning to the scene, as mentioned under Alternate Character Interpretation.
They Wasted a Perfectly Good Plot: Boba Fett is the only bounty hunter seen after Vader puts a price on Han. It would've been interesting to seem some competition between them for who can capture Solo.
Poor Captain Needa. He clearly knows he's going to die but he tries to apologise in person on the small chance Vader will be merciful and/or take the blame for losing the Falcon (which has more to do with the daringness of Han Solo than any tactical shortcoming on Needa's part) out on him personally rather than the whole ship. (It does not help when we learn, in the EU, that almost his whole family was executed shortly after his death.)
Piett. The newly promoted Admiral is fully aware of his own officers that Vader keeps killing, and the poor guy has this look on his face that screams "Oh god, I'm next." Ironically, Vader lets him live all the way through the movie and well into Return of the Jedi. In fact, when Piett does finally die, Vader has nothing to do with it. This is probably due to Kenneth Colley's excellent silent acting in many of these shots. His expression as he listens to Vader grant him his You Are in Command Now promotion while very deliberately trying not to look as Admiral Ozzel is choking to death in the background is comedy gold. Unlike the generic officers in the previous film, Piett clearly has a personality.
Vindicated by History: The film, while commercially successful, was not as popular as A New Hope when released, and Return of the Jedi was seen as a return to form after this. However, the films then started to be released on home video, and those watching it there started seeing this as better than the other two. Now it's considered the best film not only in the original trilogy, but out of all the Star Wars films in general.