kay, so I'm playing a little bit at work right now while there's no one in the office,and I'm REALLY REALLY liking the game.
The mission structure is like a folder tree in windows: You have your Shinra Power Company missions, and missions from other people. I just finished the Ifrit Materia Hunter quest, which was a short fight with Ifrit to obtain his materia. Now, I cannot arm the Ifrit materia, and it's listed in my item menu, so I can only imagine that after use, it disappears. I haven't tried it yet, though, so I'm not sure.
I do really like how the missions are sometimes long, sometimes really really short (sometimes even just a few seconds). The structure of the game was made perfectly for a handheld. They did an excellent job of making the game something where you can accomplish a goal within a small amount of time, instead of going through gigantic dungeons, and going into sleep every so often.
(the story has just begun, and it's still introducing characters, so I'll refrain from talking about it for now)
The graphical quality is wow. The facial animation is right up there with KH2, as is the body movement. Instead of using canned animations in every cutscene, SE did a great job actually doing unique animations for important cut scenes.
The battle system is a blast. I like the fact that the DMW (the slots) runs in the background while I fight. It's like a little christmas each time it hits a 7 and restores my HP, MP or AP. I definitely need to play more, but my initial impressions are that the game is not only of high quality, but does a great job of retaining the feel and ambience of FF7.