Shawn: ENTP w/ Se. He is so obviously Ne Dom, though. He may be great with sensing what's around him, but when it comes down to it, his ability to recognize patterns and analyze data make him an obvious Ne.
Gus: ISFJ. This makes sense, as he is a foil to Shawn.
Juliet: Always thought of her as an ISTJ. She has those feeling moments, but I imagine this is just poking fun at her being the only major female character in the show. For the most part, her decisions seem to reflect Te, and she never gets pushed around. Si, because she seems very conservative/traditional; rarely questions the norm.
Lassie: ESTJ, to the absolute extreme. I don't think I really need to defend my reasoning here.
Henry: (Why is the dad always named Henry? Nvm) ENTJ. Very strong Te here, with plenty of Ni to back it up, and it would make sense that he and Shawn have shadow functions.
Chief Vick: I'm gonna go with ESTJ. She has the bossiness of a Te dom, but rarely does she question the way things are done.
Since the show pretty much revolves around Shawn, it makes sense that most of the characters are SJs, since they really juxtapose his crazy Ne.