The following image shows markings that I have never seen before. Does anyone know what all those 1.C and 3.C mean?
They are scattered about on every page.

My educated guess is they mean 'una corda' and 'tre corde'. Though my score has just p and f markings.
I bet you have Schirmer

Gee, did I get in before Alf ?

Thanks, that makes sense. And no, it's not Schirmer - it's Ricordi - whatever/whoever that is; I can't remember where I got this music - it's printed in Italy is all I know. But it amazes me that they put in all these 1-cord, 3-cords markings. That's going to make playing this piece a lot different now.

I would not bother using una corda here, it seems a bit facetious and risky at that. Just do piano and forte as I think was intended.

Giulio Ricordi was an Italian publisher (now I believe that the publishing house is part of the Sony BMG group). Who's the editor of your Bolero? Beniamino Cesi or Attilio Brugnoli?

Concerning the 1C/3C indications, bear in mind that that edition is several decades old, probably conceived at the beginning of the last century. Said that, a quick comparison with my PWM/Ekier reveals that the only difference is just about those indications! And they make a lot of sense to me. You have loud repeated chords in the LH and the pedal down, how could you possibly deliver those diminuendi?

It's Brugnoli.

Yes, it makes sense to apply the una-corda pedal in all those places, but it's also very tricky. At least for me. I don't think I've ever played like that where my left foot is so busy. I'll try it, though.

In my opinion, I don't think the UC pedal should be used just to make something softer. It's always a "special effect" thing in my playing, since it changes the tone. Of course, I've recently made it a goal of mine to REALLY learn how to use the pedals, and not have the damper just simply always be used to sustain notes either. I think the most interesting playing is when the voicing/balance is all thought out and controlled, all the lines are shaped, and the pedals are used as means to a musical end rather than just to sustain or make softer... just my 2 cents!

I like your 2 cents! And you're absolutely right about the UC pedal being used more for changing tone, not volume. Using all 'three' pedals is something that I am probably going to be forever trying to improve.