Filmed back-to-back with Wishmaster 3 - La pietra del diavolo (2001). There essentially was a weekend between filming the two movies in 2000.
Both the third and fourth films were shot on a tight 16 day scheduled shoot according to the director Chris Angel.
Both the third and fourth film have been noted as going more of an Action-Fantasy route as opposed to a Horror-Fantasy genre style like the last two films. Both sequels have also been noted for their Cinemax late night programming type vibes (cheesy acting, softcore style nudity, low budget filmmaking).
The Djinn gains some wisdom in the concept of romance, in order to fulfill Lisa's wish to "love him for who he is". His solution is make her his second in command and give her a paradise to live in once his brethren are free.
The Djinn allowed Sam to walk again but didn't heal his legs. It's implied to be due to the Djinn being distracted when granting the wish.