Are there physical or psychological conditions that are a barrier to ordination to the Priesthood in the Catholic Church? It is my understanding that priests in the Old Testament, sons of Aaron, were to be without blemish. [cf. Lev 21:16-24 (RSVCE)].

In the history of Church to the present day, have there been and are there now, any comparable physical or psychological conditions that are considered a barrier to ordination to the Priesthood in the Catholic Church?
Can.  1041 The following are irregular for receiving orders:
  
  1/ a person who labors under some form of amentia or other psychic
  illness due to which, after experts have been consulted, he is judged
  unqualified to fulfill the ministry properly;
  
  2/ a person who has committed the delict of apostasy, heresy, or
  schism;
  
  3/ a person who has attempted marriage, even only civilly, while
  either impeded personally from entering marriage by a matrimonial
  bond, sacred orders, or a public perpetual vow of chastity, or with a
  woman bound by a valid marriage or restricted by the same type of vow;
  
  4/ a person who has committed voluntary homicide or procured a
  completed abortion and all those who positively cooperated in either;
  
  5/ a person who has mutilated himself [this includes vasectomy, castration, sterilization, etc.] or another gravely and
  maliciously or who has attempted suicide;
  
  6/ a person who has placed an act of orders reserved to those in the
  order of episcopate or presbyterate while either lacking that order or
  prohibited from its exercise by some declared or imposed canonical
  penalty.


(cf. the commentary on this canon)



This Instruction Concerning the Criteria for the Discernment of Vocations with regard to Persons with Homosexual Tendencies in view of their Admission to the Seminary and to Holy Orders by CONGREGATION FOR CATHOLIC EDUCATION, is an example of how Bishops, major superiors and all relevant authorities are to carry out an attentive discernment concerning the suitability of candidates for holy orders, from the time of admission to the seminary until ordination. In one section it states


  The spiritual director has the obligation to evaluate all the
  qualities of the candidate's personality and to make sure that he does
  not present disturbances of a sexual nature, which are incompatible
  with the priesthood. If a candidate practises homosexuality or
  presents deep-seated homosexual tendencies, his spiritual director as
  well as his confessor have the duty to dissuade him in conscience from
  proceeding towards ordination.