Corrected entry: The cave of wonders originally states that "only ONE may enter here" emphasizing the number one. Yet Aladdin is able to enter with Abu. And it's not that it doesn't count because he's he's an animal as it is Abu that sets off the booby traps inside. And if animals didn't matter, then Jafar could have just sent Iago inside to grab the lamp.
Correction: The emphasis on ONE does not mean just one singular person but rather a particular individual, as the Cave states "one who's rags hide a heart that is pure, a diamond in the rough", meaning Aladdin. Abu was able to enter the cave as well because he was accompanying Aladdin. Iago wouldn't be able to enter because he works for Jafar, who's heart is far from pure. It's the same reason why the cave collapsed on the thief who also worked for Jafar in the opening scene.
Corrected entry: When Jasmine is accused of stealing at the apple stand, she says she has no money. Coinage was a rarity at that time period and bartering was much more common, so why didn't the vendor or Jasmine consider those enormous gold or brass earrings and headband?
Correction: The movie is intended for children, who are unlikely to understand bartering concepts but would be familiar with money and paying for things. For trivial plot points like this it seems they tried to stick with terms and concepts that children could quickly comprehend.
Correction: Jasmine was unfamiliar with markets and, being a Princess, the concept of bartering as well. I have just watched the scene and her headband is never visible to the vendor and her earrings, while partially visible, are very close in color to her scarf; this could easily explain why the vendor failed to notice them, particularly combined with Aladdin's fast talking rescue of Jasmine distracting the vendor.
Corrected entry: Why did Jafar need the genie's help to make Jasmine fall in love with him? Being such a powerful sorcerer couldn't he have just done it himself?
Correction: Obviously he doesn't know that particular spell. Jafar can't be an expert on everything, and you wouldn't expect an evil sorceror to be particularly well up on love spells - it just doesn't fit with the whole 'evil sorceror' thing.
Corrected entry: Genie is in the palace garden trying to convince Aladdin to tell Jasmine the truth. At one point, Genie turns into a lighted lampshade on Aladdin's head. Aladdin pulls the chain to turn the light off. How did Aladdin know how to turn off a 20th century lighting device?
Correction: By seeing the chain it would be pretty obvious to Aladdin that that was what needed to be pulled to turn it off.
Correction: Aladdin has never seen a light or a lamp and has no clue how they work. Saying it would be pretty obvious that you pull the string to turn the lamp off would be a huge stretch. He would be just as likely to pull or turn the lamp shade to try and turn it off as to pull the string (which he does as if he knows exactly what it will do without hesitation). That said, this is a children's movie, and moments before that scene, genie is impersonating people who won't be born for hundreds of years. Suspension of disbelief has to be taken to extreme levels when watching cartoons or you can make an error out of just about anything.
Continuity mistake: When Jasmine wanders by the market and is shown a fish, the fin is either perpendicular or parallel to the body depending on the shot.
Suggested correction: This is simply not true, it's seen in only 2 shots and both the pelvic and the dorsal fin stay the same size, the fish is further away in the second shot and the pelvic fin changes position and looks a different size but they use the exact same drawing. Even so, the dorsal fin of a fish can change size even when dead and shaken about by the salesman. And the tail fin is only seen in 1 shot.
Stupidity: When Jasmine finds out that Prince Ali is actually the boy she met in the marketplace, she seems to completely forget about Jafar telling her he had been executed. She never asks why he's alive, nor does she even bother to confront Jafar about his treachery.
Suggested correction: The fact Aladdin was alive only told her Jafar lied about it. When she is brought back by Aladdin to the palace it is still night, not long after that she is confronted by her father and Jafar who has him under a spell. She hardly had time to ask about the treachery, probably thinking to do it in the morning. It is there and then Jafar is exposed by Aladdin. She probably wondered about it, but didn't figure out the implications yet.
Corrected entry: The rule of entering the "Cave of Wonders" spoken to Aladdin by the Cave itself is, " Touch Nothing But the Lamp". It is not until Abu snatches the ruby in the Lamp Room scene that the Cave qualifies the original edict to, " You have touched the forbidden TREASURE". Aladdin and Abu have touched the Magic Carpet plenty of times before this point.
Correction: The cave is able to determine who is "worthy" to enter through whatever mystical charms have been placed upon it. It is very likely the cave can also determine "intent", just as it has determined that Abu is Aladdins "pet" and not a second individual. Aladdin and Abu did not intend to take the carpet or other treasure they happened to inadvertently touch. It is not until Abu purposely and intentionally goes to take the ruby that the cave determines the rule has been broken.
Correction: The magic carpet was presumably an exception, as it's not really treasure but more of a guide to lead them through the cave of wonders.
Also, he did not so much "touch" with his hands as simply walk on it underfoot, couldn't entirely be helped (he comes into contact with the treasure on the floor the same way, no ill result), thereby awakening it, and further contact is initiated by Carpet himself.
Correction: It would seem the cave considers Abu a pet, so he doesn't count as a person. And as is usually the case, you are responsible for the actions of your pet, up to and including stealing magical jewels from a cave of wonders.