KH1 is the only game that has much missable content... The rest usually stuffs everything in the required viewing. Here's what I can think of right off that nobody else has mentioned yet:
- Pinocchio in the Accessory Shop prior to Monstro.
- When you're visiting worlds throughout KH1, the journal re-writes itself based on what point in that world you've reached so far. Once you complete the world, everything written before disappears and a brief write-up replaces it. *shrug* I like to see how the journal describes things sometimes.
- The guy next to the Accessory Shop's door talks about Maleficent when she visits the Town (the same time you can fight Opposite Guard Armor).
- Getting Blizzard from the Cheshire Cat prior to the trial.
- You can get treasures from blowing out all the lamps at Olympus Coliseum with Blizzara and then another chest when you do it with Blizzaga. I guess you can miss the Blizzara chest if you've already upgraded? I assume the same is true for the treasure chests you get from defeating Heartless in the first room you drop into in Wonderland. I believe there's 3 chests you can get there, but maybe just 2. There's a new chest every time the Heartless that appear there change. I usually go back there right after visiting Lotus Forest the first time, fight the Heartless that's there. Then they change again after Alice disappears, so I go back again (or you can wait until the world's already over). Then they change again after the first visit to Hollow Bastion.
- Blowing open the blocked entrance during the Pot Scorpion battle so that all of the Agrabah marketplace is open to battle (and 10 thousand pots attack you everytime you enter a new room). The people that appear post-Jafar before you leave the world.
- Changing text bubbles throughout world events. Sometimes this means running back and forth unnecessarily to see their comments. (This is also true for KH2.)
- You can miss the Donald & Goofy scenes in the 2nd District where they're looking for Leon, if you run back to Cid as soon as you see the scene of the Heartless being created from some NPC's heart.
- After you play on the swing with Pooh, he'll appear on a log and you can light the fire in front of him to get a prize.
- A cutscene of Peter Pan knocking on door of the room that Wendy's locked inside.
- The different scenes based on whether you lose or win against Leon in Traverse Town and Cloud in the first visit to the Coliseum.
- Anything with Tidus / Wakka / Selphie on Destiny Islands, including the Sora v. all three fight.
- Leon, Yuffie, and Aerith in the First District after the scenes at the hotel but before beating Guard Armor. Aerith gives you a Megalixir, I think?
- Leon, Yuffie, and Aerith standing around in the cafe after your first visit to Traverse Town, talking about the Dalmatians. They'll disappear when you return for the 2nd visit. Actually, I can't quite remember if you automatically go to the world map after beating Guard Armor; that little scene may only be available before you leave the world after beating Guard Armor.
- SDG's first meeting with Seifer and co. in Twilight Town. I believe if you go straight to the train station to meet Mickey, you can miss it completely?
- Visiting Belle after you free the servants but before you talk to Beast / visiting Belle after Beast loses the rose but before fighting Xaldin.