Technically, I think the characters are all E or at least moderates for the sake of television. It's hard to make a really reserved, quiet character interesting and enjoyable. Technically, a lot of characters are sort of inconsistent and unrealistic since this is probably a moderate to low budget TV show.
Zach - ESTP/ESFP... typical cool guy, who likes action and is excellent at dealing with crisis situations. He doubles as an ESFP because he's not mean and is willing to be friends with Screech.
Slater - ESTx.... a jock who isn't aimless and undisciplined. I can't quite call him ESTJ due to his lack of ever being in charge.
Screech - INFP/INTP.... sometimes plays the role of nice, sweet, well-connected (or more so than an INTP) idealist and sometimes plays the role of a stereotypical, science-loving nerd who makes all kinds of social blunders. They beef up his I to ambiversion because real I isn't good for television as I mentioned before.
Kelly - xSFJ.... sweet and responsible girl who is popular, although, doesn't want to be popular that badly. She likes fun but is dedicated to fulfilling her responsibilities more so.
Lisa - ESFJ.... what matters is fashion and popularity... likes typical ESFJ stuff like celebrities and gossip.
Jessie - xSTJ... she has a strong sense of how things should be and a strong, assertive personality. She is dedicated, goal-directed, and responsible. She is generally not interested in kindness, helping people, people-related things in general, so I give her a T.