Doctor Parnassus - INFP
Tony - ESTP
Valentina - ENFP
Anton - INFP
Percy - INTJ? certainly a J
Mr. Nick - I'll guess INTP, but might be any kind of NT

Any opinions?

I expected more from the movie, but the outbursts of Gilliam's imagination were fascinating as usual. I loved Doctor Parnassus's character and especially the the "story goes on and on" theme (what a pity it wasn't used to its full potential).