My guess is that Korah and the others were somewhat regretful for challenging Moses' leadership and claiming that he was simply seeking after his own glory.  It seems that many leaders, at some time or another, have their motives questioned by their followers, and I appreciate the example that Moses gives to us.  I think there are several leadership lessons that we can take from this reading.

1. If you're doing what God wants you to do, then you don't need to make any apologies.  As long as you have that confidence, then boldly lead.  It is not prideful or arrogant to do what God asks you to do.
2. Grassroots movements of people questioning your leadership should be dealt with swiftly (that is, if you're confident that God is leading you).  If Moses hadn't dealt with the mutiny on hand, the whole nation could have been wiped out because of their faithlessness.  However, Moses was able to stop the tragedy from spreading to the entire people.
3. God will be your defender.  Notice that Moses didn't defend himself before the people; he allowed God to defend him.  He dealt swiftly with the issue, but he used the opportunity to bring things before the Lord, and he allowed the Lord to step in.