Here's yet another rules query:

What happens when you exhaust a Support card that doesn't have "exhaust to perform X" as part of its cost? Does this negate the card's ability or does it have no effect?

I'll give 2 examples:

1) Shotgun

While attached character is committed to a story, it gains "Action: Pay 1 to choose and wound a character committed to this story."

2) Atwood Science Hall

Characters you control get +1 skill for each I icon they have.

So, err, what happens when these card are exhausted (by a character or card effect)? Can they even be targets of effects that exhaust Support cards, or must you target a Support card that has "exhaust" in its card text (i.e. Derby Hall or Mi-Go Scalpel)? I'm guessing that any Support card can be targeted, and by exhausting it any abilities it confers are unavailable until the card is refreshed. However, it's a source of debate in my gaming group so any assistance in resolving this problem would be greatly appreciated.

Thanks in advance for your help.

Nothing bad happens to a support card when it is exhausted. The only thing is that it can't exhaust to pay for things. If the card doesn't have an exhaust payment (Atwood, for example), then it works as normal when it is exhausted.