When most people start using the Butterfly Guard in BJJ (Brazilian Jiu-Jitsu) and/or submission grappling, they make one or all of these 3 mistakes.
The first mistake in the Butterfly Guard is to lie flat. Although a few very talented people CAN play guard in this way, you are much more mobile and powerful when you're sitting up, and your guard is also much harder to pass.
The second most common Butterfly Guard mistake is not gripfighting. Anytime you allow your opponent to get a grip on you, you give him an opportunity to control you and pass your guard. So, regardless of whether he's grabbing your feet, legs, head, wrist or lapel you should gripfight, gripfight, gripfight.
The third most common error is not having a plan for each range of the Butterfly Guard. You need to know how to be offensive (i.e. which primarily means having sweeping options) at long, medium and close range.