Coach of the team on defense calls "time out!!"
 

very emphatically, and play is stopped. I immediately know that I've screwed up. Is there a penalty for that? or is it just a correctable mistake by the official?

No penalty, (unless he's out of time-outs), just grant the time-out and get ready to get an earful from the other coach.

Not aware of anyway to correct it
 

I've done the same damn thing once!:)

5-8-3 Situation E

Once granted it cannot be revoked, although I've seen it treated as an IW & play on.

The only penalty is that he now has 1 fewer timeout left. :)

Valuable lesson learned ... always look to see who is requesting the T.O. before blowing the whistle. Probably most officials have done it at least once in their career.

This is how we treated it.

Count me as one! :(

Then, tail between your legs, go over to the other coach and explain the rule. That's how I handled it anyhow. (thankfully, it was Rec Ball).