The application of qualified immunity clearly stems from the principle that sometimes one causes accidental harm when doing the right thing. It's most reasonably stated as an extension of good samaritan laws. The problem isn't the principle itself but rather how and when it gets applied.
> Are there any examples
Your house catches fire, you're unconscious from smoke inhalation, and your daughter is trapped in her bedroom by the blaze. Emergency responders decide to enter your home to rescue you and your daughter. On the way in, one of them breaks something very important to you. Can you sue for damages? Can you sue for trespassing? Did they "break and enter" your home?
> Are there any examples
Your house catches fire, you're unconscious from smoke inhalation, and your daughter is trapped in her bedroom by the blaze. Emergency responders decide to enter your home to rescue you and your daughter. On the way in, one of them breaks something very important to you. Can you sue for damages? Can you sue for trespassing? Did they "break and enter" your home?