Here are some Mutations I've been thinking about.
I totally agree on the Thick Skinned mutation. Adding in DT at the expense of Agility or Charisma, or Agility and Charisma (with names perhaps like Thick Skinned, Leatherface, Carapace for various levels of DT like light, leather, and combat armor equivalents).
Then there's a Sight-related sequence called I've been thinking about, Here's Lookin' At You, where you can gain Vision powers (Eagle Eye=binocular vision; Bug-Eyes=EM vision; Eyes-of-the-Beyond=toggle-able Night/Heat/EM visions). I'd give Charisma penalties at least for Eyes-of-the-Beyond, for the player being a "weirdo" and always staring off "into space".
I was thinking a Mutation where you had lighter bones might be fun for someone to play, kind of like the Small Frame perk, but giving you rather significant levels of increased speed, perhaps a doubled jumping and falling ability, but with significantly higher critical chance in damage done to you. Haven't thought of a name for this idea yet. I see an agile, sleek, very fast, high-jumping and high-falling shooter who has to keep his/her distance from danger OR ELSE...and I wouldn't think it too overpowered, either, as any grenade should really pulp you up as well, so you're susceptible to ranged weapons, too, you're just a harder-to-hit target.
Random ideas I had on Anvil Fists was that you should be able to bash open locked containers and doors. You wouldn't make any friends in Rivet City or Megaton, but getting in places shouldn't be a problem.
I was also idly wondering if you could interject some form of inherent danger in the mutation system, not that you should, mind you, just thinking, kind of like having a FEV meter like the Radiation meter, and at the change in critical levels you get your points to spend (although I don't know how that would work with the Rapid Mutation), and at what was the Death point for a normal player at 1000pts of Radiation, 1000 pts of unused FEV would turn you into something like a Failed FEV subject who just couldn't keep up with the FEV and started "losing it". Of course, you'd lose your character at that point as you'd lost all of what you were.