Why does Ed not pursue the origin of the fake Philosopher's stone used by Cornello?
I'm getting all of the following information from episode 3 of Fullmetal Alchemist Brotherhood.

Near the end of the episode, Ed exposed Cornello as a liar to all his people.  Cornello attempts to kill Ed using his alchemy.  During the attempt, Cornello's alchemy "rebounds" and causes some ... adverse effects on Cornello.  After a short fight, Cornello's fake stone breaks.  Ed starts asking about it and Cornello states he knows nothing about it.

Given all that, I don't believe Ed didn't think it wasn't important, but that he had nowhere to go with that.  First, the stone was gone and couldn't help Ed learn anything.  Cornello was equally useless in learning about the stone.

On top of that, a real stone would have allowed Cornello or Ed to do whatever they wanted, presumably without any rebounding.  This made the fake stone even less desirable for two reasons.  First, there is no guarantee that it could even help Ed and Al (granted there was a chance, but it may not have been worth the time to look into).  Secondly, even if Ed did get his hands on a fake stone, there was no telling if it would rebound and just make matters worse.

Overall, it's not that it wasn't important, just that Ed had no leads on where or how to get a fake stone and that the risk might not have been worth it.