How to catch duplicate comments In my sites comments are moderated so (anonymous) visitors sometimes get confused and try to resubmit it. 
It happenens within say 5 minutes only.

What is the best way to catch and reject duplicate comments by the same user?

One way is to look for same body text from same session within say 5 minutes and reject it.
I'm not aware of any module that would provide this particular functionality. First of all, I would reduce the risk for confusion. An example is: Store a CID in the users $_SESSION, and theme the comment form with "You have X comments awaiting moderation."

You could also add a custom validation function to the comment form with a hook_form_ID_alter, and simply deny comments that fall within your stated condition, "Same body text within 5 minutes from same session", or so.

I would definitely focus on the first one though. No matter what type of validation criteria you add, there will always be edge cases where there is a good reason for posting something that your will then reject. This will of-course be a tradeoff between how large a risk you are willing to take rejecting valid input, and the effor required to "un-confuse" users.