Some delicious copypasta, but relevant:

In one scene, Genie calls Al's clothes "so 3rd century." Genie has been trapped in the lamp for 10,000 years, so there's no way he could know of the fashion trends which have happened since he's been trapped. Which means the latest Genie could have been trapped in the lamp is the 3rd century. If he spent 10,000 years in there, it is now AT LEAST the year 10,300 AD when he gets out.

Aladdin takes place IN THE FUTURE. A post-apocalyptic world where only Arab culture (and some Greek) survived. It has been so long that the name "Arabia" has been corrupted to "Agrabah." The Muslim religion has atrophied to the point where there are no mosques, Imams, or prayer mats, but people still give praise to Allah in moments of happiness. Amazing technological marvels left behind by the previous civilization, like sentient flying carpets or genetically engineered parrots which comprehend human speech instead of just mimic it, are taken for granted by the locals or considered "magic."

The Genie proves this by making impressions of ancient, long-dead celebrities like Groucho Marx, Jack Nicholson, etc.