You have to remember that Family Guy has a track record for being crass, politically incorrect, and controversial. That said, I actually enjoyed the episode, though I too found it rather gross. There was a strange pseudorealism to it, though. Everything you call pointless is pointless for a reason. Everything they did when they were drunk, they did because they were drunk and had impaired thought processes. Thus the piercing and it subsequently going horribly wrong, the argument, all that.
You also have to remember that we're dealing with a baby and a dog here, neither of whom are the sharpest tools in the shed. You can't expect a lot of "intelligent" humor, especially not with this show.