I love this show. It's the only thing I watch regularly. Hmm...
I agree he's probably an ISTJ, though anxiety and depressive disorders will make people seem more ISTJ anyway.
Stottlemeyer: ISTJ, or ESTJ, maybe ISTP... actually I'm finding him very hard to pin down, perhaps because we rarely see him outside of work, where he's in a position of authority and responsibility, and he seems to want to keep up appearances a lot of the time. He's got to seem organised, sensible and composed, and doesn't want people guessing just what he's thinking.
Randy Disher: ENFP or ENTP, maybe borderline.
Sharona: ESTP, weakly T
Natalie: ESFJ, weakly E and S
Having seen interviews with them and read about them I think Tony Shalhoub (Monk) is probably ENFJ and Jason Gray-Stanford (Disher) almost definitely ENFP. Not seen enough of the others to say, though Ted Levine seems pretty I--P and Traylor Howard (Natalie) F.