Can an unsuccessful grade appeal hurt an academic career?
Can a grade appeal that is not granted affect a person's transcript,
  reputation and/or perception throughout their academic career?


I have never heard of a school that lists grade appeals on a student's transcript, and to me that sounds about as logical as listing on your transcript that you wore the wrong shirt color. But that doesn't prove that such a school doesn't exist, so only a professor or staff member at your school can give an authoritative answer to that question. Why don't you ask them?

As for affecting your reputation or people's perception of you: well, any interaction we have with other people has some potential to affect our reputation or people's perception of us, so the literal answer to your question is "yes." It's reasonable to worry about that a little bit, but on the other hand if we all spent too much time worrying about such things, we'd never get very much done. In your case, what I suggest is that you go to your professor (or email him) and explain that you are surprised by your grade and would like to understand why you got an F, among other reasons so that you can learn from the experience and do better next time. Ask if you can review your final exam and possibly go over it with him to understand what you got wrong. Don't sound like you are assuming that you deserve a better grade or that the F grade couldn't possibly be correct, since that could come across as entitled, arrogant, and possibly delusional. If you ask the question in such a way, I don't see how you can possibly leave a bad impression with the professor -- this is a reasonable request that most professors hear all the time and are usually happy to help with.