I would suggest that enough upvotes would negate the flags. Build an algarithm that determines at a ratio when to waive the flag's penalty. And that's a great idea, if someone is flagged enough from multiple posts, there should be punishment. A possible punishment idea would to suspend the account for X amount of minutes. However, this could cause united attacks on posts, which may cause harm, but allow to view who flagged what content. If that person is notorious for flagging for false reasons, that person should be penalized per some sort of Terms of Service causing grief.
Just talking off my head here.
There should be a flag for content posted in the wrong section and one for spam type content and one when you feel the user has copied or plagiarized. And yes the second part of that should be true as you've said to prevent people from falsely using the alert/flag system.