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There is a way to "broke" the Transmog on Weapons by using the new "Current Specialization Only" and Illusions making the weapon take a random transmog, even on the Character Selection Screen, until you Relog the Character,
Steps to Replicate:
Erase the Transmog on a Weapon that is Transmoged and has an Enchant Illusion. (Don't erase the Illusion) Make sure the "All Specializations" is selected.
Transmog the Weapon to something without changing the Enchant Illusion, but this time select "Current Specialization Only".
Change Specialization, it should Transmog into something else.
Examples:
Rogue Tank Spec Confirmed!!1:
There you can see my Rogue with her new "Shield". It appears that the bug makes every 1H Weapon into the same shield: Large Metal Shield Large Metal Shield
Tried this with an 1h Axe/Sword and a Dagger.
The Shield isn't even Transmogable in the first place.
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Invisible 2H Weapon:
There you can see my Paladin with an Invisible 2H Mace because it has the apparance of the Nomadic Bracers Nomadic Bracers
Tried this with a 2h Mace and a Polearm.
The bracer isn't even in the game.
This for obvious reason appears to not work on Weapons that can't have Illusions. (Ranged and Shields).
Other people can also see it.