Does the text on Hero cards that say "So-and-so may use an additional power this turn" mean that that hero can use the same powe twice on that turn?
No. You cannot use the same power on a single card twice a turn unless the card explicitly says so, like Overdrive.
If you have two different cards in play, for example two Stun Bolts, then you can use the Stun Bolt power from each separate card with the additional power use.
Awesome, thank you! That's the way I've been playing it, I just wanted to clarify.
More generally, an effect that gives you a *specific* power use lets you use that power even if the "one use of a power per turn" would normally prevent it.
One significant example of this is with Expatriette. If she has Pride and Prejudice out, and is the recipient of a "may use an additional power" during her turn, she may (and probably should) do as follows:
* Use Prejudice (first power use).
* Use Pride (additional power use).
* Use Prejudice (because this is explicitly allowed by Pride, that overrides the normal once-per-turn rule).
When using Unload, save Pride until last, and you can get an extra use of Prejudice on top of all the power-uses that Unload allowed you.