FFVI: Divergent Paths

I think I may have found the problem. You said that you first noticed this after Leo spoke to Lola. When you recruited Leo, did you have:
1. 4 members in your party
2. One of them Mog
3. But not Shadow, Gau, or Gogo?

In that specific set of circumstances, a typo would activate in the event script that, instead of checking for 4 characters in the party, would check for character #4 (Shadow). If he was not in your party, The script would force out the actor with the highest character ID, which, in absence of Gau ($0B) or Gogo ($0C), would be Mog ($0A). however, it wouldn't properly dispose of his object, and if he were supposed to be displayed as the main character, would keep him in the last pose he was in during the event scene (facing downward). Reloading the game from a save file would refresh all of the objects correctly, fixing the issue.

I will fix this in the next patch. It is seen as a low priority for now.