Yea, the Duty tab was where I found the 12 for Praetorium. But I just figured out what I did wrong. After skipping all the cut scenes and actually getting back into the game I immediately went to the inn so I could catch up on everything, before I actually turned in The Ultimate Weapon quest. I just turned that in and now at the inn that quest is available in the journal and it has the remaining cut scenes. It's a little silly, considering the conversation you have with Minfilia when turning in the quest references things that happened in the cut scenes, but thems the breaks I suppose.

They really need to just kill the instance timer when people are viewing cut scenes so they're not pressured to skip them.