The oath is a significant, serious requirement. The inventor must sign an oath, and this should be the last thing done before the application is filed. Make it a habit to get the assignment done at this time also.
What should you do if you spot a typo after the oath is signed? Don’t simply change it; what you file must be what was the subject of the oath. If it is in fact a typo, file the original as signed, then also at the time of filing file a preliminary amendment fixing the typo. If it is more material than a typo, fix it and get the oath resigned.