A few years ago I watched Spain v Ukraine in Seville. There was a group of Ukrainian lads sitting near us necking beer after beer. I'm sure they didn't realise it alcohol-free.
Are you sure they were pistachio shells and not sunflower seeds? Usually in Spain it's sunflower seeds during the match then at halftime foil-wrapped bocadillos appear in the hands of every fan in the ground. Always at halftime. Never a second before or after.
It's the home of paella so you've got to go for one. Lunchtime is best. I'd recommend making a booking as the best places fill up. Do your research- even in Valencia I'm sure there are lots of places churning out 2nd rate paella.