What does Canon Law say about Bishops? How are suitable priests identified, nominated and chosen?
Can. 377 §1. The Supreme Pontiff freely appoints bishops or confirms those legitimately elected.
§2. At least every three years, bishops of an ecclesiastical province or, where circumstances suggest it, of a conference of bishops, are in common counsel and in secret to compose a list of presbyters, even including members of institutes of consecrated life, who are more suitable for the episcopate. They are to send it to the Apostolic See, without prejudice to the right of each bishop individually to make known to the Apostolic See the names of presbyters whom he considers worthy of and suited to the episcopal function.
§3. Unless it is legitimately established otherwise, whenever a diocesan or coadjutor bishop must be appointed, as regards what is called the ternus to be proposed to the Apostolic See, the pontifical legate is to seek individually and to communicate to the Apostolic See together with his own opinion the suggestions of the metropolitan and suffragans of the province to which the diocese to be provided for belongs or with which it is joined in some grouping, and the suggestions of the president of the conference of bishops. The pontifical legate, moreover, is to hear some members of the college of consultors and cathedral chapter and, if he judges it expedient, is also to seek individually and in secret the opinion of others from both the secular and non-secular clergy and from laity outstanding in wisdom.
§4. Unless other provision has been legitimately made, a diocesan bishop who judges that an auxiliary should be given to his diocese is to propose to the Apostolic See a list of at least three presbyters more suitable for this office.
§5. In the future, no rights and privileges of election, nomination, presentation, or designation of bishops are granted to civil authorities.
Can. 378 §1. In regard to the suitability of a candidate for the episcopacy, it is required that he is:
1/ outstanding in solid faith, good morals, piety, zeal for souls, wisdom, prudence, and human virtues, and endowed with other qualities which make him suitable to fulfill the office in question;
2/ of good reputation;
3/ at least thirty-Five years old;
4/ ordained to the presbyterate for at least Five years;
5/ in possession of a doctorate or at least a licentiate in sacred scripture, theology, or canon law from an institute of higher studies approved by the Apostolic See, or at least truly expert in the same disciplines.
Canon 377 §2 confirms that there is a list of episcopabile prepared by the Bishops' Conference every three years. However secret, there is a discussion among existing Bishops, and this means that if any of the priests suggested as potentially suitable to become a Bishop has traits of character which might make him unsuitable, and which are known to one or more of the Bishops taking part in the discussion, then that trait should be taken into account.
Separately, when a particular vacancy is to be filled, according to Canon 377 §3 it is the responsibility of the Nuncio to seek opinions from appropriate Bishops (all of whom are likely to have taken part in the discussions above) and the diocesan Chapter. He doesn't have to consult anybody else if he doesn't want to. However, the requirement in Canon 378 §1/2 for a suitable candidate to be of good reputation, separate from the requirement for him to be good faith, morals, piety, zeal, wisdom and prudence, surely means that both the Bishops' Conference triennial meeting and the Nuncio's investigation in respect of a particular see, must act to investigate any suggestion that a candidate's reputation is not good.
It is sad that a good and holy priest about whom there have been unjustified rumours should be excluded, at least temporarily, from consideration for the episcopate, but that's better than allowing to be consecrated somebody about whom the rumours, while not verifiable, turn out to be true.