I just noticed a difference in the wording of these two cards:

'Faceless Abductor' says:

Action : Shuffle Faceless Abductor into your deck to choose a non-Ancient One character with skill 3 or less. Return that character to it's owner's hand.

'One of the Thousand' says:

Action : Shuffle One of the Thousand into its owner's deck to lower the cost of the next character you play this phase by 1 (to a minimum of 1).

I think the Abductor should use the latter wording, too, since it still works correctly if the controller of the card changes. Currently, if I take control of my opponent's Faceless Abductor, I'd have to shuffle it into _my_ deck, which doesn't really work. OR is that already covered by the FAQ's section on 'Gaining Control'?

When you have taken control of a card,
you are considered to be that card’s
controller, but not its owner. When that
card leaves play for any reason, or at the
end of the game, you must return it to
its owner. If it leaves play as the result of
a game or card effect, it is returned to its
owner’s control, but still is placed out of
play. So, for example, if the card would
be sent to a discard pile, it is placed in its
owner’s discard pile.

I think I'm starting to think too complicated, since I was wondering if I could even use the Abductor's Action if I took control of it...

I agree with you. Abductor should read "Owner's deck", otherwise, as written, it sounds like you could steal someone's Adbuctor and put into into your own deck - not the owner's deck.

Many things are not worded consistently across cards, not just in CoC but probably all CCGs/LCGs.

In some cases, the designers may actually want minor nuances to be different, but this doesn't strike me as one of those, I think it was accidental. Thinking as a designer, to justify two wordings the payoff in terms of added interestingness has to outweigh the added complexity of having two versions and possible player confusion/mistakes. In this case, I don't think it does, so I'd vote for a consistent wording.

I just realized the wording on Faceless Abductor. So I have a question:

The cost is to shuffle into "your" deck, but if a player takes control of it, wouldn't it be impossible to pay the cost of the ability since it would never go into "your" deck, but rather control would pass back to the owner? And if it returns to the owner, would it just be discarded? Or could you not even attempt to trigger the effect since you can't pay the cost?

Interesting question. I think I'd have to go with "unable to pay" here.