1) Equipping the Avenger Sword while in combat doesn't change the attack power... you will have the attack power of the 
previously held weapon. If you were to have Cecil at max stats (99 STR and 96+ AGI at level 99), swapping the Crystal Sword 
for the Avenger Sword will allow you to deal an average of 9000 damage. This bug goes away after the battle is over. 
In theory, this tactic is relatively overpowered. This is fixed in FF4A AFAIK.

2) If the Avenger Sword is equipped before the battle with Zeromus, particularly on Cecil, he is forever stuck in that battle.
AFAIK, FF4A has this bug "fixed" where "Berserk" status is uninflictable until post-Zeromus change.

On a related FF4A change, if Charm is inflicted on the wielder, Berserk status is removed... though this seems specific 
to FF4A. Also, Black Hole removes this status completely in FF4A. FF2/4 continues to reapply the status under both instances...

3) There are some peculiar properties with the Charm status, especially when afflicted on the Avenger Sword wielder 
(this doesn't apply to Berserk since it is not possible otherwise). The first attack made while under Charm actually hits 
the enemy... sometimes continues for a longer duration but eventually follows proper Charm targeting...


The guy wielding the Avenger Sword will not attack until the characters preceding him in the attacking order
executes a command. After the preceding character executes a command, the Avenger Sword user attacks like a normal 
Berserked user.

The only exception here though is if the wielder of said weapon is in the first attacking slot (middle).

This bug does not occur in FF4A.

Addtionally, if the Avenger Sword wielder is coming off Charm, the character is reberserked when his turn comes up... 
so they may be stuck doing nothing for several turns.