Development Hell: Walt Disney himself commissioned an early storyboard that hedged much closer to the Andersen original, which the crew of the final version eventually discovered. You can see these sketches on the recent DVD.
Executive Meddling: Jefferey Katzenberg caused the animators and others working on the film quite a bit of grief. One memorable instance was his insistence that the whole "Part of Your World" sequence be excised from the film, saying that he found it "boring" and also because he saw a child drop a box of popcorn during that moment in a test screening. Animator Glen Keane eventually persuaded Katzenberg to let them test the film again with that scene intact, and the positive response convinced Katzenberg to leave it in.
Genius Bonus: Ursula's incantation for casting the spell on Ariel includes the words "Laryngitis" and "Glossitis". Someone well-versed in medical terminology would notice that they are a rather common conditions that may result in mute-ness.
In the sequel, Tip is voiced by Max Casella and Wataru Takagi in English and Japanese, respectively. Both also provided a voice in the Jak and Daxter games; Daxter and Pecker, respectively. This is ironic, as both characters are enemies, and often fight with one another.
And don't forget that Undertow is Baron Praxis; in this film, he eats Daxter!
The Other Darrin: Flounder has been replaced various times during the franchise, due to being (most of the time) voiced by a real kid. Jason Marin played him in the first film. Edan Gross played him for the first half of the television series, and was replaced with Bradley Pierce. Courtland Mead voiced him for merchandise released in the `90s (including the Animated Storybook CD-ROM, as well as a few toys), Cam Clarke voiced him in the sequel (due to him being an adult), and Parker Gloris played him in the prequel and the Kingdom Hearts series.
Ursula was originally intended to be played by Divine, who died before he could record the role. Bea Arthur turned down the role because she was busy with The Golden Girls, and Jennifer Saunders auditioned but didn't get the role.
In addition, Melissa Fahn was originally supposed to play the role of Ariel, but was beat out by Jodi Benson.
A deleted draft detailing an alternate version of the ending had Ariel and Flounder trying to rush to the wedding barge only for Glut (the shark from earlier in the film who got stuck in an anchor ring) to ambush them, causing Flounder to gain a second wind, deliver an already exhausted Ariel to the ship, and bait Glut into chasing him with the barrel still lassoed onto his back (hint: it's actually a gunpowder barrel), causing Glut to bite the barrel and get caught in an explosion.
Broadway singer Elaine Stritch was the original voice of Ursula, but her constant clashing with the crew had her fired and replaced with Pat Carroll.
Ariel was imagined as a blonde early on, but the animators didn't want to be seen as ripping off Splash too closely.
During the production of Ariel's Beginning: a storyboard◊ from the film was presented. It appears that someone has Eric, Ariel and Sebastian hunting for a white whale and Sebastian isn't happy about it. There's also a woman in the storyboard who gets seasick like Grimsby in the beginning of the first film. It's implied that some talking parrot character will not get along with Sebastian and it's also stated that Ariel and Sebastian are "still angry with Eric". This was intended for another idea called "Ariel’s Undersea Adventures".
Fun Fact: Jodi Benson, the original Ariel, and Sierra Boggess, who originated the role on Broadway, both graduated from Millikin University.
One of the models they used as a reference for Ariel's movements was Sherri Stoner, who would go on to voice Slappy Squirrel in Animaniacs. That's right: Slappy Squirrel was Ariel. Try wrapping your brain around THAT one...