Genie only officially granted the wish to be made free
Of the other two wishes, one was in progress but never fulfilled and the other was not official since it was never verbalized.
Wish 1 - Genie never makes Aladdin a prince
Aladdin wishes for Genie to make him a prince. Genie then grants him a menagerie and all sorts of other fancy things to make him look like a prince, but he is not officially a prince as is pretty well established throughout the rest of the movie.
The only way for Aladdin to become a prince is to marry a princess. So Genie is still in the process of granting Aladdin's first wish the entire movie.
Genie tries to convince Aladdin to tell Jasmine the truth about not being a prince in order to woo her
Genie: All right, Sparky, here's the deal. If you wanna court the little lady, you gotta be a straight shooter. Do you got it?
Genie: Tell her the truth!
Aladdin: No way. If Jasmine found out I was really some crummy street rat, she'd laugh at me.
Jafar exposes Aladdin as a non-prince
Jafar: ♪ Prince Ali, yes, it is he. But not as you know him! Read my lips and coms to grips with the reality. Yes, meet a blast from your past, whose lies were too good to last! Say hello to your precious Ali! ♪
Iago: Or should we say Aladdin?
Aladdin: Jasmine, I tried to tell you. I'm just...
Jafar: ♪ So Ali turns out to be merely Aladdin! Just a con. Need I go on? Take it from me.
The Sultan has to make a new law so that Aladdin and Jasmine can get married
Genie: No matter what anybody says, you'll always be a prince to me.
Sultan: That's right. You've certainly proven your worth as far as I'm concerned. It's that law that's the problem.
Sultan: Well, am I Sultan or am I Sultan? From this day forth, the princess shall marry whomever she deems worthy.
At this point Genie has already been set free so it could safely be said that he has not granted Aladdin's wish of being made a prince before being set free. A change in the law actually has to be made so that Jasmine and Aladdin can get married. Its also worth noting that they do not get married until the third movie Aladdin and the King of Thieves
Wish 2 - Aladdin doesn't officially wish to be saved from drowning
Genie can't grant an official wish unless Aladdin says the words, "I wish for [blank]", but this doesn't limit Genie's ability to intervene. There are two examples in the movie of Genie performing acts on Aladdin's behalf which Aladdin didn't verbally wish for.
Unofficial wish #1
First, Aladdin tricks Genie into getting them out of the Cave of Wonders, which Genie accepts was not an official wish due to this logic.
Aladdin: Ah, no. I never actually wished to get out of the cave. You did that on your own.
Genie: Well, I feel sheepish. All right, you baaad boy, but no more freebies.
Aladdin: Fair deal.
Unoffical wish #2
When Aladdin is drowning, Genie saves him but since Aladdin is unconscious he is unable to make an actual wish. Genie even tells him that he can't save him unless he says the words. But this would appear to be untrue as he immediately goes ahead and saves him anyway after Aladdin appears to nod.
Genie: Never fails. Get in the bath and there's a rub at the lamp. Hello? Al? [gasping] Al! Kid, snap out of it. You can't cheat on this one. I can't help unless you make a wish. You have to say, "Genie, I want you to save my life." Got it? Okay! Come on, Aladdin! I'll take that as a yes.
It has been argued that this second wish was official because of the original agreement of "no more freebies", however it is already established that Genie does have the ability to intervene without there being an actual wish made. I don't see any evidence in the film or otherwise that the "no more freebies" agreement was binding in any way that would eliminate Genie's ability to perform an action without a wish being made.
In addition, I would argue that Genie was already obligated to save Aladdin from drowning due to Aladdin's wish to be made a prince which had yet to be fulfilled.
So, Genie never grants Aladdin's first wish to made a prince. Aladdin only becomes a prince after he marries Jasmine, which he doesn't do until the third movie and is only able to do because the Sultan changes the law.
The wish to save Aladdin from drowning was non-binding because:
- Genie was obligated to save him because he had not yet fulfilled the first wish to make Aladdin a prince
- While Genie and Aladdin had a verbal agreement of "no more freebies", it is established that for the wish to be official, Aladdin must say the words, which he doesn't do.
- It is also established that Genie does have the ability to intervene without a wish being official