I generated a mutant with, among other things, one extra (right) arm. Later in the game, I quaffed a mysterious liquid that gave me another extra arm. Here's the problem: the second extra arm appeared at the bottom of the Traits column on the character sheet, but can't be found in the inventory/equipment screen.

How am I supposed to roleplay a walking crime against nature with only three arms?

It definitely should give you another extra arm. Just tested it, and it worked as intended. Not sure what's going on there, as there is no real limit to the number of limbs you can have yet.