Here are a few, most of which you all will probably think I'm crazy for even listing.
1. This one's easy to reproduce, but it may not be worth even considering. If a character levels up (physical level or job level) as the very last move in a battle, the little jingle will prevent the main music from fading out as it's supposed to at the end. The music plays for a bit longer then suddenly changes to the Victory theme. Maybe I'm the only one who immediately noticed this the first time I played the game back in the day.
2. If you open a character's ability list while in battle, the music slows to half speed and the character sprites stop moving. This was on my PSP, so it's possible it's just an issue with the emulation.
3. I actually posted this (erroneously) in another thread, mostly as a joke, but it's a legit glitch I would say. Not sure how easy it is to fix.
Anyway, As a side note, if a character has a) Dual Wield, b) the Blood Sword as their first weapon, and c) low health, attacking an Undead monster (or, I presume, attacking any monster if the character also has Undead status) results in the character dying after the first attack (as expected); however, the character suddenly springs back to life for the second attack animation, though it doesn't even register with the game (it plays the sound effect as if you attacked air and the monster doesn't dodge or anything). Afterwards, the character falls back down.
Probably inconsequential as it doesn't result in any abuse (that I can think of) or gameplay weirdness. It's mostly just weird.
4. Not sure if this is intended or not, but it's possible to target a character with an item who is directly above you in a multi-height stage, regardless of the height. I tried this on the Execution Site map and had my Time Mage use an item on my Dragoon who was standing several levels directly above the Time Mage (under that archway). For the life of me, I can't recall if Item has any height restrictions anyway, but it seemed unnatural.