In response to Robertus, even the offhand hits cannot crit unless its its specified as the tp mod or in mighty strikes. Spikes in damage otherwise are either good rolls on pdif Bonuses or double or triple attacks.
Many tests were made with Asuran fists and others, but no WS damage made it out of the expected max range pDIF or DA/TA(not able to on Asuran Fists) allowed.
Blade: Jin has a tp mod of "Chance of Critical varies with tp", so Jin will have an improved chance to critical on each hit with this katana.
Blade: Ku on the other hand, has "Accuracy varies with tp" so it is not possible for it to critical on any hits of the WS regardless of the bonus on this weapon.
For higher level ninja, sadly, it is now obselete.
HOWEVER, and there has to be a however for this, it has served myself, and many other ninja well for years.
For newer high level ninja, until you get your "Trial of the Magian's" weapon, if you have the free time or patience to break it do so, you won't regret it.
Although just a side note, i personally have not experienced abyssea yet but i have heard of lower levels going in and leveling rapidly, and perhaps those Ninja will not benefit from this weapon as they will bypass it almost all together. Seems such a shame, this weapon was once a ninja's best friend, although an excuse to use this again could be level 75 capped events and the like as the 75 trial weapons are usually obselete to this (Assuming the 80/85 weapons are synced to their 75 previous versions).