I am not sure whether it is that relevant if you are only talking about a motion. A motion is simply a party's request for something. An Order or Judgment is what would be signed by the judge. That is when a ruling is made ON a pending motion. If you had a motion filed requesting a review of custody... you can always file another motion.
However, if a motion was filed with the Clerk, it should be recorded and still be in the file. Whoever filed the motion (whichever party to the case) can file a Corrected Motion if they made an error in the original one, but the first one should still be on file with the Clerk and in the original court file. So, while technically, there could be a filing problem with the Clerk's office, it is really not that relevant to the decisions by the Court. The judge doesn't sign a motion. Judges sign Orders/Judgments (Final Order, Order of Modification, Final Judgment, Summary Judgement, etc). And with any order signed by the Judge, a copy of it is provided to each party (or their respective attorney). I am a little confused, because I just don't see how, even if someone DID do something improper, it is relevant to the review of custody. If your ex asked for the review, and no longer wants it but you do, then YOU file for it. Again, a "Motion" is simply the request.