Does the red bird have a special ability?

From everything I've seen, the red bird is still just the same base bird with no special abilities as it was in past games. When you tap on the screen it makes a noise, but it doesn't seem to change anything about the flight path, which is similar to the other versions.

The shockwave you see when tapping appears to be cosmetic only. I ran a couple of tests on level 1-1 and triggered the shockwave right next to the pig without hitting it, and it didn't cause the pig to die or move at all.

Yes apparently, by July 2013, an update of the original Angry Birds included Red's Mighty Feathers which Red (that's actually his official name) finally has its own ability: Changing direction of flight. Here's the video how it works

The little shockwave from the red bird does effect the pig. It makes the pig jump! This make the pigs hit the ground real hard causing it to pop or damage the pig.The green bird(Terence or the red bird brother) also have this shockwave but its a lot stronger. You just need the right timing and the right distance.