Since you mentioned this, you should also play FF4:TAY and THAT game has a LOT of missable items. These are the big ones that matter.
All the challenge dungeon stuff. (Nearly impossible to miss but you can still miss it)
Small tails (most important missable, FOLLOW A GUIDE)
Many summons. Matter of fact there's only a few that you can't miss. Chocobo is the easiest one to miss. Find it on a remote island during the first part of The Crystals chapter. During the same chapter you'll fight other summons periodically. Make sure not to kill any of them. They surrender at low health but if you kill them they're gone forever. And make sure to get the 4 dropped summons in Rydia's chapter (goblin, mindflayer, cockatrice, bomb) they are not able to be found later.
You can miss several characters. Proceed along the next 3 spoilers with caution.
calca and brina from Rydia's tale can be missed. You need a few items from the cave at the end before you beat the final fight of that chapter to keep them. They kinda suck though so no big deal.
all of the eblan 4 ninjas can be killed on their solo missions. Once they reunite with Edge you're in the clear.
MAJOR SPOILER man in black can die during the fight with the Dark knight unless your party includes Cecil, Man in black, Rosa, and Ceodore. This is the only way to keep him alive.
as soon as hooded man joins your party, kill him and just leave him dead the whole game. Eventually you'll reach a point where Hooded man does a solo fight. His stat progression changes after this fight but his level does not so you lose quite a lot of stats by leveling him up first. Note that the fight at minimum level is kinda hard and you'll need to do things like use the defend command lmao. You can level him up normally after that.
As soon as you start the lunarians' chapter, it will take you into a battle. Go to the item menu and unequip your sword.
As soon as you get control of Cecil for the first time, unequip all his shit (grind him to max level while he's alone first otherwise you'll find running around with naked Cecil is impossible). The sword can't be used by anyone but Cecil however Ceodore can use his armor.
I think there are some missable steals. Check an item guide.