The owl in the title sequence is computer generated. The first attempt at a photo-realistic CGI animal character in a feature film.
The various things that Jareth does with the crystal balls (rolling them around his arms and in his hands and so forth) are not camera tricks or any other kind of special effect. They are actually done by choreographer Michael Moschen, who is an accomplished juggler. Moschen was actually crouched behind David Bowie with his arm(s) replacing Bowie's. Unlike a typical Muppet performance, however, he had no video screen to view his performance. In other words, his manipulations were performed completely blind.
One of the reasons why Hoggle is always making groaning noises between lines was to keep his mouth open as much as possible, so that actress Shari Weiser was able to look out.
In the scene where Toby (Toby Froud) is seated on Goblin King Jareth's (David Bowie's) lap, the baby has a fixed and hypnotized look off-camera as Jareth murmurs evilly into his ear. In fact, Toby screamed so much during the many takes of this scene, that something had to be done to keep him quiet. Fortunately, a crew member had a glove-puppet Sooty. For the duration of Jareth's speech, David Bowie had the Sooty puppet on one hand (out of shot) gently wiggling to distract Toby. The child was entranced, hence the hypnotic stare, and the perfect silence.
The sources of the characters can be seen in Sarah's bedroom at the beginning of the movie. She has a stuffed animal that looks like Sir Didymus on her dresser, a doll that looks like Ludo on the shelves next to her door (along with the book "Where the Wild Things Are" as the camera pans across her desk), a Firey doll on a shelves next to her bed, bookends with Goblins reminiscent of Hoggle on her dresser, and a figurine of Jareth on the right hand side of her desk. After you see the Hoggle bookend, there is a scrapbook shown. It shows newspaper clippings of Sarah's famous actress mom with another man, David Bowie. In addition, the dress that she wears in the ballroom scene can also be seen adorning the miniature doll in her music box, and a wooden maze game on her dresser next to her books is reminiscent of the hedge section of the Labyrinth. There is also a small painting on her wall that depicts a contraption much like the one operated by the "Cleaners" from which Sarah and Hoggle had to escape. And there is a copy of the famous picture by M.C. Escher which is used in the room where the final confrontation with Jareth occurs.