For a run-through on the wishes...
Escaping the Cave: Aladdin uses his cunning to trick the genie into getting him out of the cave, Genie accepts he's been out-witted, but no more freebies.
Turn me into a Prince: This wish goes through mostly, but Jasmine hates Prince Ali's bombastic entrance, so Aladdin still has to win Jasmine over, Aladdin can't expose that the Genie actually makes him into a Prince, and the cast gradually find out the truth as the film progresses (Jasmine catches Aladdin out during the Whole New World sequence, Jafar catches him out when he sees Aladdin has the Lamp)
Save from Drowning: Forced wish Aladdin has to make after the Royal Guard nearly kill him on Jafars orders (Jafars Hypnotism on the guards? I can't exactly remember this part).
At this point, Jafar gets expelled, Aladdin and Jasmine are in love, all is well, but the Sultan drops that Aladdin will become the next Sultan and rule Agrabah and it's people, which is way too much for him to handle. He has no idea how to handle this and feels that he may have to use his final wish just to get himself out of this situation, thus breaking his promise to the Genie. Shortly afterwards, Iago steals the lamp and gives it Jafar, making Jafar the master now and Jafar will keep an iron clutch on the Lamp as best as he can.
Jafar wishes to be Sultan (No one respects him as Sultan though) then wishes to be a Sorceror (So people will respect him), Jafar exposes Aladdin's lie and un-princes Aladdin. and then sends him flying (Carpet gets Aladdin back to Agrabah), after a confrontation Jafar then get's tricked by Aladdin into using his last wish to become a Genie (Jafar's undoing), Aladdin get's ownership of the Lamp back. The law is still in effect, Genie offers Aladdin to make a prince again but Aladdin has a change of heart and needs to be who he really is, no more lies, and wishes for Genie's Freedom. Sultan after seeing this Selfless act abolishes the law saying only princes can marry the princess and the two get happily married ever after the end until Return of Jafar.