102F is related to escaping. The data there is modified when using Porom's Cry command. My thought is that it is some type of internal "Luck" stat, that is used when determining whether the party can escape, and maybe other times.
The data from 102D-F is calculated during the equipment initialization, so it could be immunities for the other statuses; however, those statuses don't really need immunities (Barrier, Wall, image, jumping, hiding, etc.). Also, the values don't really seem to support this. At the beginning of the game, the values for Cecil at 102D-E are 02 and 14, which would imply immunity to Stop, image high, and Wall. Since we know this isn't true, it must be something else.
They could be related to the other equipment bits. Since they're buggy it's difficult to test. However, the 102D-F data comes from within the character stats; the bits that control metallic/throwable/etc. are stored within the equipment data, meaning they are calculated from the equipment. It's unlikely that equipment data would be stored within the character stat data. This is why I think those three bytes may be some internal "Luck" stat, or something to that effect.
Absolutely ancient, but still here's a required Bump!
I've figured out what the 102D-F (or at least one of the bytes) do. Phoenix was right on the mark. It's kind of like a "luck" stat. 102D Definitely is. What 102D actually appears to be is the chance to Critical Hit.
It appears to be Value = Chance to Critical Hit - And it may be just a plain 100 (setting it to 64 seems to almost always guarantee a critical hit) rather than based off of 255. Now oddly this test was done with the Dummied Crystal Sword copy, which would mean that Logically I should have No Crit chance, but setting that to 64 and FF produced critical hits a plenty.
So Value = Chance to Critical Hit x Attack Multipliers. At least it appears that way and a Critical Hit seems to be recorded differently for each hit whether it was a Critical Hit or not. (not graphically speaking however)
NOTE: All Shadow Party people come back with the same critical hit stat, including Adult Rydia (who should have none due to being equipped with a Property 1 Weapon)
Dark Knight Cecil - 02 (14 0A)
Kain - 02 (14 0A)
Rydia - 01 (28 0A) - (So from the very start Rydia is given less of a chance to Critical Hit... hah.)
Tellah - 01 (1E 0A)
Edward - 02 (1E 0A)
Rosa - 02 (3C 0A)
Yang - 01 (Wha?!) (32 0A)
Palom - 01 (1E 0A)
Porom - 01 (1E 0A)
Paladin Cecil - 03 (I thought as much) (1E 01) - (01? Hmm...)
Cid - 05 (Whoa.) (23 14) - (Very different values from everyone thus far. I wonder what they mean...)
Edge - 08 (Well, I guess he's the king of crits then.) (19 19)
FuSoYa - 00 (Eh?) (00 32)
And there you have it. Edge will crit more than anyone else and it seems that FuSoYa cannot naturally get a critical hit Ever. To my knowledge some of this flies in the face of conventional knowledge. Exactly how does Property 1 make it so you can't critical hit then?
Well I figured out the first byte, let's see if I can soon figure out the second.

Here's a peculiarity.
Cecil clearly has a 02 14 but in battle (and indeed viewing his initial battle records) this stat is shown as 04 19, hmm...
Ah hah... part of it is weapon based... each weapon may have its own Critical Hit Modifier...

2 Shadow - x2 +05 (Yes, you're reading that right. The Shadow Blade gives x2 to your current Critical Hit Modifier, tested with Critical Hit at 2, then at 5. At 2 it rises to 4, and 5 it rises to A. The second value seems to be a static +5 though.
Darkness - x2 +10
Black - x2 + 15
Note: It seems that the second value increases in comparison to its base attack power. Meaning that this value will be (Character Innate + Half of the weapon's Attack Power). I still have yet to reason out what this does...
Ah! I see! What it actually does is decide the amount of extra damage a weapon will deal when it Critically Hits. Setting the value to FF made that abundantly clear. That surprisingly means that Rosa has the best Innate damage with Critical Hits, oddly enough, with Cid in a close second and of all people Rydia in a distant third.
I should probably start from the beginning...
Now to see if all weapons do is double the chance for Critical Hits of if there's more to it...
Nothing - x1
Claws - x2
Rods - x2
Staffs - x2
Dark Swords - x2
Light Swords - x2
Swords - x2
Spears - x2
Ninja Swords - x2
Knives - x2
Whips -x2 (though they should not be able to cause Critical Hits due to Property 1, they still add the normal x2 which is inherent to all weapons so far)
Axes - x2
Throwing Weapons - x2
Boomerangs -x2
Harps - x2
Hammers - x2
Bows&Arrows x3 (Quite a shock!)
(Quite Possibly the game penalizes dual wielders by taking away their Crit Bonus from a normal weapon.)
Well aside from the discovery about the bows that felt like a waste so...
The critical hit bonus is basically double of what is shown above.
And confirmed! Characters who equip two weapons Lose their Critical Bonus when dual wielding! While quite significant for Edge, Yang barely seems like he will be able to score any critical hit in the first place.
Now all that remains is that final byte... it never appears to change and seems unique for some characters.