my school of though is that we cannot effect the MIX of the PA speakers.
Well, technically both correct and incorrect. The engineer is setting the levels, but they are, in fact, human beings, subject to error, and in many cases, can have certain sound issues brought to their attention, which they can then effect. Roughly 99% of my recording is in small venues, either near or far. In the local venues, every sound guy knows me, knows what I do, and generally knows that I have a fairly good idea of what I am talking about, so they tend to listen and make adjustments. I also tend to personally know many of the bands that I record, and frequently their traveling sound guys, and have no issue letting them know if something really sounds amiss.
Remember all we are doing is placing mics in an ideal place at the good height and recording. Our quality recordings greatly depend on the mix done by the engineer.
See above. Even if you cannot or fear approaching the sound guy, you can effect your recording substantially by relocating or reorienting your mics, to deal with the sonic issues that you are encountering.
This is an over simplification because mic placement and positioning (not to mention the actual mics) can make a huge difference but I can't imagine packing my headphones with me when recording though my 09hr and ca14 cards.
Yes, and having the admitted luxury of a 722, with a headphone preamp that allows me to hear everything, along with excellent headphones in terms of both isolation and reproduction, as well as TLM-170s, with switchable polar patterns and bass roll-off, I can make significant changes to my recording, even without the cooperation of a sound guy.
For those who always take headphones, what would you do if there was too much guitar or bass in the PA mix?
See above, but in most small locations bass is rarely in the mix at all. Too much guitar might lead me to a wider pattern, so that the PA sound was coming furhter off axis.
What if the high EQ levels sucked or the lows?
Again, see above, but EQ can usually be adequately addressed in post.
What if the vocals were low in comparison to the instruments?
Once again, see above, but otherwise, I might relocate or reorient my mics so that they are getting as much as possible from one or both PA stacks.
How would you fix this pre-post with your headphones while recoding?
I can't fix the lack of vocals in post, which is another classic demonstration of why I want to hear what's going into the deck, so that I don't go home, and find a bassy show, with weak vocals, and a really loud booming kick drum coming from the subs. You can't recreate a lack of vocals after the fact, so you either need to say something, or do something, otherwise, you might as well turn off your gear, and just listen to the show.