Well, I think I got the use of the word short and open circuit confused since a short is:
Short:
An electrical short or a short circuit is a problem which occurs when an accidental path is created in a circuit, generating a connection where one did not exist before.
I don't think in the case of my mouse an extra electrical connection is being made, or an accidental path crossed, so I think I am safe to keep using this. The short is in the connector end that runs to the computer, because if you apply pressure there it works perfectly, so I know the buttons work.