Other than a bar grievance how would litigants respond to their adversary filing papers and not sending them copy?
The litigants could request in a motion to the court that any action taken based upon the filing of the documents be set aside, could move for an extension of time based upon non-service of the papers, and could move to strike the documents, depending upon the circumstances. The remedy would depend to some extent on what was not served and what consequences that had and whether the person not served could have known to check the court file because they would have expected to be served.
Of course, there are a few kinds of papers that can be filed in litigation ex parte without giving advanced notice to the other party, such as a motion to hold someone in contempt of court, a motion for a temporary restraining order, and certain kinds of property seizure or arrest orders where disclosure would impair the ability of the person carrying out process to do so.
If the documents not sent were initial service of process in a case, failure to give notice might be jurisdictional, although this is not true in every case (e.g. in a probate or bankruptcy case, notice to another interested party with the same kind of interest is often sufficient to bar a challenge by a party who didn't receive notice).