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.
Accidental Innuendo: The movie has a famous example of unintentional innuendo in the song "A Whole New World."
I can open your eyes, Take you wonder by wonder; Over, sideways and under On a magic carpet ride. A whole new world! A new, fantastic point of view. No one to tell us no, or where to go, Or say we're only dreaming. ... Unbelievable sights! Indescribable feeling! ... A whole new world! Don't you dare close your eyes. A hundred thousand things to see. Hold your breath — it gets better!
Well at least the song has a happy ending. At the end, they hold hands as literal fireworks are shown going off.
Adaptation Displacement: Did you know that in the original tale, Aladdin had unlimited wishes instead of just three? Or that he had a second genie in a magic ring? Chances are that you don't.
Again when Agrabah was reintroduced in Kingdom Hearts II. When Sora, Donald, and Goofy arrive, Iago finds them, and warns them of a Heartless ambush. In exchange, he asks for Sora to put in a good word for him to Jasmine and Aladdin. Iago then guiltily tells Sora and Aladdin where Jafar's lamp is, in the Cave of Wonders, only to discover that the Peddler got it first. Pete then steals it from him, and Sora gets it back. During the second visit, Iago lures Sora and Aladdin to the ruins, while Jafar takes over Agrabah.
Iago is also useful in a "World Runner" deck in the short-lived Kingdom Hearts card game. He appeared in the fourth and final American set, as a level 0 (Meaning he can be played if you have no other friend cards in the friend area.) If you discard him, you can remove a Heartless card from your current Agrabah world card. Which is helpful, because two of the three Agrabah cards have no dark limit, meaning your opponent can play as many Dark or Nobody cards as they wish on your world, and some of them have little means of being extinguished.
Surprisingly, the Carpet is also one. It was even popular enough to have been made into a Xbox Live Avatar prop.
Also hilarious right away considering Jafar's living conditions at the end of the movie.
Aladdin and Jasmine's world tour in "A Whole New World" includes visits to Greece and China (the latter even with fireworks); in the former case, given the subsequent cartoon crossover, that would suggest Hercules himself was around at the time.
The first lyrics in "Friend Like Me" include a reference to the Forty Thieves. Flash forward to the third movie and learn that Aladdin's father is their leader (and would've been during the first movie's events).
In the same vein, a woman in "One Jump Ahead" says "I'd blame parents, except he hasn't got'em".
In one scene of the first movie, Jafar deceives Jasmine into believing that Aladdin has been executed "by beheading" (while Al is actually alive and imprisoned). In the first sequel, Al is condemned to death by decapitation, and nearly beheaded by Public Execution when Genie arrives in time to save him in a Big Damn Heroes moment. In the TV series's episode, Al finally gets his head "cut off" by Caliph Kapok... or rather separated, since the rest of Al's body is still alive while his friends find a way to reunite it with his head. Weird.
Some Moral Guardians made a stink over a bit in the balcony scene where Aladdin seems to be saying "Good teenagers, take off your clothes."
Deviantart artists that likes drawing Bound and Gagged people usually would have a field day on alternating the scene where Aladdin is ambushed, Bound and Gagged by Jafar's men and tossed to the sea until he accidentally rubs Genie's lamp under the sea, saving his life. They just replace Aladdin with any character they like, and either stop before the character 'rubs a lamp'... or use an equivalent of Genie to save the day.
Moral Event Horizon: After Aladdin gives Jafar the lamp, he leaves him to die in the Cave of Wonders.
Narm: "Are You In Or Out" in King of Thieves is supposed to show the remnants of the Forty Thieves planning to return to their bloodthirsty rampaging roots after Cassim reformed them into Noble Demons. But it's hard to take some of them seriously since several of them are still humorous in design, and the lyrics include "I'm the prince of generosity" and "Imagine the fear on their faces / when we drop by for cookies and tea."
Painful Rhyme: "His forty fakirs, his cooks, his bakers"... Ouch. note 'Fakir' in English is usually pronounced "fah-KEER", or maybe "FAY-KEER", but not the same as "faker".
Well, technically, since all those people are just creations of the Genie, they're all fakers.
Smurfette Breakout: Jasmine is a supporting character while the story is about Aladdin, but she is included in the Disney Princess franchise and is actually the only princess in the lineup who isn't the main character in her film.
Squick: Jafar isn't particularly attractive on his own, but any scene where he puts advances on Jasmine makes him look even slimier, causing major squick! Even in the movie's own universe, Abu and Iago have a Squick noise at Jasmine and Jafar's kiss. Jasmine looks pretty grossed out as well during that.