Is there an option for mediation or a third party?

Also if you purchased the home on the California Residential Purchase Agreement then most likely you signed Pg8 Section 22 Item B which is the Arbitration clause which means you will need a neutral party to mediate the issue.However I agree with @Scott Carder if the repair is not very expensive 1k to 2k it might be easier and less stressful to just fix it and let it go.

We would be looking outside the mediation/arbitration.we are interested in  practical experience, in a general partnership, as how to move forward when both partners have different ideas.ei; tie breaker....Thank you in advance!

Now facing mediation in law suit within 2 weeks. 

And my point is 1% would ever see the interior or a courtroom in a full blown trial.these things all get settled in mediation or arbitration that's my personal experience. and you can have all the asset protection you want but if someone sues you   you still have to pay to defend.. they may not collect the judgement but your still out the defense dollars right ? 

You have no way to mediate this unless you want to knock on the neighbors door and talk to them in person.

A mediator was also there to help me.

Mold exposure generally doesn't kill, but will make people sick...In 2004 the Institute of Medicine (IOM) found there was sufficient evidence to link indoor exposure to mold with upper respiratory tract symptoms, cough, and wheeze in otherwise healthy people; with asthma symptoms in people with asthma; and with hypersensitivity pneumonitis in individuals susceptible to that immune-mediated conditionLead exposure generally doesn't kill either, it just causes brain damage and other fun things to happen...The signs and symptoms of lead poisoning in children may include: Developmental delayLearning difficultiesIrritabilityLoss of appetiteWeight lossSluggishness and fatigueAbdominal painVomitingConstipationHearing lossBabies who are exposed to lead before birth may experience: Learning difficultiesSlowed growthAlthough children are primarily at risk, lead poisoning is also dangerous for adults.

If I were you I'd sit down with the agent's broker and lay out the entire situation and see what s/he says - a sort of informal mediation.

They've already tried mediation.