George Lucas hated the process of scripting the first film, so he hired noted pulp SF novel author and Golden Age Hollywood screenwriter Leigh Brackett to write the script for Empire. She wrote one draft, but died of cancer soon afterwards. As a result, Lucas wrote the next few drafts himself, before asking Lawrence Kasdan to do revisions. Incidentally, the famous Luke, I Am Your Father reveal wasn't in Brackett's draft; Lucas only added it when he started rewriting the script himself. Although most of her version was rewritten, two contributions by Brackett did end up making it into to the final film: the planet names 'Hoth' and 'Bespin'.
Yoda almost suffered this in the prequels because George Lucas originally asked Jim Henson to play him.
Creator Backlash: George Lucas called Empire "the worst Star Wars film". Yes, really. Though, then again, problems with filming and its original reception need to be remembered, since at the time of its release the film was considered worse than the original by critics and many moviegoers.
Creator Cameo: The Aryan-esque Imperial officer who uses Leia as a body shield during the Bespin firefight with Luke is actor Jeremy Bulloch, who spends the rest of his scenes in the movie playing Boba Fett in face-concealing armor. The choice to use him as the officer was less about letting him show his face on-screen than that he fit the blond, blue-eyed Nazi type they thought was appropriate and was already on set.
Enforced Method Acting: When shooting the big scene between Luke and Vader, David Prowse said "No, Obi-Wan killed your father", and that's what the entire crew of the film thought would be said when James Earl Jones dubbed in his lines. Only 5 people (Lucas, Jones, Mark Hamill so he would react correctly, writer Lawrence Kasdan, and director Irvin Kershner) knew the actual line.
And Hamill didn't know until they were on set and ready to film. Kershner took him aside and told him moments before. They were very determined to keep the big reveal a secret.
According to a 2016 interview with Mark Hamill, the extreme precautions turned out to be totally justified; not long after the scene was filmed, newspapers were reporting the "big twist" of Obi-Wan killing Luke's father - meaning someone on the set that day went and blabbed.
Executive Meddling: Defied. George Lucas wanted an opening scroll for Empire Strikes Back to match the one he did for Star Wars. The Director's Guild of America attempted to force Lucas to have opening credits instead.note During this time, it was required to have the credits in the opening to give proper due to the director of the film. The Guild gave Lucas a free pass with the first film because he was the director himself, but since Lucas had someone else direct Empire, they were no longer letting him off the hook. Long story short, Lucas decided to quit the guild and form his own studio so he'd never have to deal with the meddling from guilds again.
It Will Never Catch On: Despite the surprising and massive success of Star Wars, there were serious doubts that the sequel would be anywhere near as good. Irvin Kershner nearly turned down the director's chair because he felt he could never make it as anything other than "the second one." His agent convinced him otherwise, and now Empire is almost universally acclaimed as the best film in the saga.
Lying Creator: To make absolutely sure the big twist wouldn't leak, only Lucas, Irvin Kershner, James Earl Jones, and Mark Hamill knew about the real line, with the script featuring Vader saying "Obi Wan killed your father." The rest of the cast and crew only learned the truth at the movie's premiere, and David Prowse was quite upset with Lucas afterwards, saying his physical acting would have been completely different if he'd known the real line.
A theatrical trailer narrated by Harrison Ford features C-3PO ripping a decal off a door. This is from a Deleted Scene where 3PO tricks some Stormtroopers into walking into a Wampa containment room.
There was also a shot where Vader leans forward for some reason (supposedly after his fight with Luke, as if to throw him off himself). Some speculate that this is from him trying to use the Force to pull Luke back up to him, a scene described in the children's picture book of the movie.
Not to mention a completely different shot of Luke and Leia making out. Notably, they appear to be alone in this scene, as opposed to the one in the film proper which was in front of the regular gang. Maybe the filmmakers were just shipteasing, or (less likely, considering how we know the writing process went) they were trying to throw off the scent of the twist in the next film.
The Other Darrin: The original Emperor hologram was played by Elaine Baker and voiced by Clive Revill. The DVD changed him to Ian McDiarmid, who played the Emperor in the other films.
Throw It In: When they just couldn't get Han's response to Leia in their last scene right, Irvin finally just told Harrison to get in character and they would just run the scene without him being given a line to see how he would react, and he just blurted out "I know." The original line was "I love you, too." Ford argued that Han Solo would never say such a thing directly, much less repeat someone. Lucas and Kershner agreed.
It went over budget and behind schedule, and the Hoth location shoot in Norway was plagued by a strong snowstorm and overcharges by the locals (who knew they had to cash in, given the success of the predecessor; Lucas shot Return of the Jedi under a fake name to avert this price gouging).
The Yoda puppet was made of a less-than-optimal material, resulting in it being quite a bit heavier than what Frank Oz was used to from his time with the Muppets. The strain put on his arms meant the scenes had to be shot on a quite erratic schedule.
In Leigh Brackett's initial script draft, Vader is explicitly not Luke's father; Anakin appears to Luke on Dagobah as a Force Ghost, alongside Obi-Wan. As well, it's revealed that Luke has a twin sister: not Leia, but someone else called Nellith. She's mentioned but never seen, in what was intended as a Sequel Hook for later episodes (note the plural). This was probably what Lucas had in mind when he inserted the "there is another" line. Then Brackett died, and the filming on Empire was so chaotic that he decided to wrap up the saga with only one more film, which led him to make the "other" into somebody we already knew and turn Vader into Anakin (while also developing backstory that would later inspire the prequels).
An earlier draft had Luke's reason for not leaving with Lando & Chewie at the end being that his Jedi training was more important. Believing that this would make Luke seem less sympathetic, Irvin Kershner had it changed to where Luke was still recovering from his injuries and that rescuing Han would be his first priority once he was fully recovered.
Lucas originally approached Jim Henson to play Yoda (the film was being made at the Elstree Studios complex in England, as was The Muppet Show). As he was throughout most of his life, Henson was extraordinarily busy and couldn't take the job, but he suggested his long time partner Frank Oz, and the rest is history.
David Lynch was offered the director's chair at one point.