When either party in any case in any probate court lodges objections to any proceeding or decision in the case, affecting the real merits of the case, the party making the same shall offer the objections in writing, which shall be signed by himself or his attorney and, if the same are overruled by the court, the party may petition the superior court for a writ of certiorari, in which petition he shall plainly, fully, and distinctly set forth the errors complained of. If the court deems the objections to be sufficient, it shall forthwith issue a writ of certiorari, directed to the judge of the probate court, requiring him to certify and send up to the superior court, at the time specified in the writ, all the proceedings in the case.