Question

What type of person would be a bad choice for a mediator during a negotiation

Answer 1

An impartial person makes a bad mediator. They may be impartial because of implicit or explicit biases. 

People who struggle to make objective observations, or want to preach their opinion make bad mediators. The purpose of mediation is to seek out the root cause of a problem between two parties, so the mediator must remain objective. 

A nervous person, or a (for lack of a better word) weak person makes for a poor mediator. Mediators need to remain assertive, even if the parties whom they mediate become angry (or if the parties being mediated withdraw). The mediator's job is to provide clarity to each side's thoughts, which requires both sides to speak openly, and freely. Allowing one side to dominate the conversation, or allowing one side to give up when it's clear that an amicable solution has not been reached, makes a mediator bad. 

People that don't fluently speak the primary language of those being mediated also would make a bad mediator. How can they mediate that which they don't understand? 

There are probably thousands of character traits with which you could answer this question.