I recently acquired a batcave, and i noticed something strange:
it has no limitations on whom you can assign it. it costs 10 points per character, but it does not specify who you can assign it to, friendly characters, ally characters, or enemies for that matter. it also states that regardless of assignments, only friendly characters get the benefit of using the defensive dial, or more specifically, friendly characters can use a power described on the defense dial against an enemy character assigned with the cave. to that end, an extremely simple team designed to stop almost anything:
1 batcave, 100 points,
1 m10 iron man, 225
any avengers ATA, rounding him up to 230,
and bam, within a 400 point game, you can negate enemy damage on up to seven enemies. now for clarity sake, how does this work in tournament, do the extra assignment slots at 10 points a piece go onto any 7 enemies you can find, or am I overlooking something?

I don't think the Batcave works that way.
Even the IG says "...assign to A character" with no mention whatsoever as to friendly or foe.

However, page 21 of the official 2013 rule book says a resource can not be used by an opposing player, which pretty much addresses that whole deal.

Additionally, I was under the impression that the offence dial was used by the assigned character(s) and the defence dial worked against your opponent.

Am I correct?

the offense dial allows all assigned characters to use the power listed, the defense dial shuts a power down for opposing characters. as an example, on click 1 all assigned characters gain perplex, and no opposing character may use pulse wave. incidentally, if they cannot use it, can it still be assigned to them regardless if i wanted to burn points?

What? How the heck would you be able to assign something to another player's build? "Oh, I assign my Batcave to your force, so now you're overbuilt and disqualified. Good game."

I got a good chuckle over that myself
Not poking fun at the OP, but can you imagine a quicker game?!

Worlds finals, player A plops down some disgusting Spiral team (with GH most likely); player B beats this by causing player A to exceed build total.....A is DQ'd and we have ourselves a new world champ....

.......who then proceeds to create a new 'unbroken' Spiral and balance is returned to Clix.

Well played B, well played indeed.

Im pretty sure you can't assign resources to anything but YOUR team/character(s). Period.