See http://www.thefreedictionary.com/person, definition 3: "The composite of characteristics that make up an individual personality; the self."
The point of the sentence says that Jesus is righteous in 3 distinct ways or areas: in his person, in the administration of his office, and in the discharge of his commission. That is, he is not only righteous in how he carries out his job, but the nature of his personality is to be righteous.
The applicable definition here is somewhat different from "You look shabby in your person." In that case, by "person" you would presumably mean his body, not his character as here. Typically the word "person" is used in that sense -- the "body" sense, I mean -- in statements like, "He carried his passport on his person", meaning, he actually carried it around with him in his pocket or some such, as opposed to leaving it in a desk drawer or having it in a briefcase. (I think someone would be unlikely to say "You look shabby in your person" because there's no other way you could look shabby. I suppose you might say that if you were contrasting a metaphorical use of "shabby" to describe someone's personality.)