Author Existence Failure: 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'.
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.
This could also just be either George trolling again, or the quote was taken out of context. Which, considering this fandom, would not be surprising.
It's even possible he meant it. Empire has a much bigger focus on character and dialogue, and a smaller focus on spectacle, than the rest of the OT and the entirety of the PT. Given Lucas's possessiveness of the franchise and how differently Empire feels from the rest of the saga, which he had a deeper involvement with, it's not hard to see why he might not be fond of the film.
In the DVD commentary for The Empire Strikes Back he compliments the way Kershner shot the duel between Luke and Vader so his comments about it being the worst could very have well been disingenuous.
Creator Cameo: The Aryan-esque Imperial officer who uses Leia as a body shield during the Bespin firefight with Luke is actor Jeremey 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.
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.
Last-Second Word Swap: 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.
The Other Darrin/Re Cut: The original Emperor hologram was a woman with superimposed chimpanzee eyes and the voice of Clive Revill. The DVD changed him to Ian McDiarmid, who played the Emperor in the other films. (and was one of the few changes no one complained about!)
No one complained about the actor change, but quite a few people complained about the changes that added unnecessary clunky exposition which implied Vader had no idea that this kid named Skywalker from Tattooine who'd been paling around with Obi-Wan Kenobi was any relation to Anakin (which tracks with the Emperor's lies during Revenge of the Sith and the deliberate pretense that Padme had died pregnant, but makes Vader's specific fixation on catching Skywalker earlier in Empire seem odd)
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.
Troubled Production: 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.
What Could Have Been: 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 Back Story that would later inspire the prequels).
Also, 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 directly across the street from the headquarters for 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.