I don't know, Elliott seems very "J" to me. Particularly in the beginning seasons. Again, it's hard to tell as she has inconsistent writing, but in the beginning she was very organized bookworm-like and had issues breaking that mold. In the later seasons it seems as though she did a flip from INFJ to ISFX. I really hate that they switched her character. No character development is always better than bad character development.
After considering it more, I'll have to agree with Dr. Cox as an ENTJ. He exudes Te like the world would die without it. I'd say he has a fairly well-developped P side though. I like Carla as ESFJ though. She's very traditional in her desires and very materialistic in her needs. Jordan, while definitely an I (it appears that I missed that assessment on the website), is perhaps more ISTJ. Again, she exudes Te to an extent and I like tertiary Fi for her, but I'm not sure about the N. She changes throughout the series as well, though I think it's more believable. Like Dr. Cox I believe her P side is fairly well-developped.
Nurse Roberts works as an ISTP, thinking about it more. Ted... Eh, either works for him. He's been beaten down so much that it's hard to tell. I think I like NF more for him than NT however.