Tire Rubbing Against Chainstay The specifics: 

Have an older Litespeed Vortex (2005) frame.  I think back in these days the super skinny 20mm tires were in vogue.  Anyways it seems like the frame might be super optimized towards these skinnier sizes?  I put 25mm tires on and now when I'm out of the saddle on the downstroke I can hear an ever so faint rub for a second.  

How dangerous is this situation - can I try tightening the quick release on the back wheel down super tight - or possibly something else?

Thanks :D
Assuming the wheel is good (is fully seated and centered properly in the dropouts and is true; if you spin it along its axis, there shouldn't be lateral movement) you shouldn't be running a tire that rubs on the frame. This can eat out the paint of the frame, the frame, and/or the tire. 

Try moving to a different tire (possibly a smaller one, like a 700x23) if the wheel is good. Remember that you need some space between the tire and the frame, since the bicycle flexes under load (damaged frames can flex more than the undamaged frame, so might be something to check up on).