In The Resistance is it always a bad idea for the spies to fail the first mission?
No.

You should almost never let the first mission succeed as a spy. So what if your opponents know that one of the participants is a spy? They don't know which one, and they won't be able to win without figuring out which of you it is.

By making the first mission fail, you give your opponents fewer opportunities to make mistakes as the game progresses. This greatly outweighs the fact that failing a later mission reveals less information.

You do need to get your acting skills into high gear immediately after the mission is revealed as a failure, however. You have to pretend it's obvious to you that your mission-mate was a spy, and appear extremely frustrated if the other players side with her. This can be challenging, but you can't afford to sacrifice a victory point to avoid it.