One I've heard is it's Bono kind of venting frustrations about being stereotyped as the "80's Bono," and not seen as anything but a zealot determined to make the world a better place. He's taking a stab at all the press and paparazzi that were so obsessed with U2's 80's image, telling them that they're not, (and maybe never were), what they appeared to be back then.
"Don't believe what you hear, Don't believe what you see," sounds like a warning to listeners about the gossip collums and entertainment news tendencies to make up lies.
It could also be saying that, although the band may look to be a certain way, they aren't necessarily like that.
"What happened to your face of melting snow? Now it looks like this!" Suggests a loss of innocence. U2 is no longer the 'nice' band they appeared to be in the 80's.
"And you can swallow, or you can spit, you can throw it up, or choke on it," You can accept the change in U2's style, or you can let them fade away.
"And you can dream, so dream out loud," We're still just as earnest as we were -- still saying what we feel.
"And don't let the bastards grind you down." Don't let others (the press, for this interpretaion) devalue your creativity.
I can't be bothered explaining more. I think that's pretty clear anyway.
But, as always, this isn't the only plausible interpretation. I don't even like it that much.