Corrected entry: In the movie all of the guards have swords. The blades design is basically small near the hilt (the handle of the sword), and gradually gets wider and rounder near the end of it. Well, the sheath (the carrying case) of the sword is the same shape as the sword. Because of this, it would be impossible for the swords to be slid back into the sheath, the reason being that the larger end of the blade would not fit through the top of the case, for it's too small.
Corrected entry: When the apple vendor threatens to cut off Jasmine's hand, Aladdin rushes in, grabs the sword from the vendor, and hands it to Jasmine, who hides the sword behind her back. Immediately following, Aladdin takes Jasmine by the shoulders and says "I've been looking all over for you." Notice that her hands are now in front of her and the sword is nowhere to be seen.
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.
Corrected entry: When Abu is on the bursting lava rocks in the Cave of Wonders, right before the last two rocks blow up you can hear him say "Holy shit", if you turn your volume up.