Buyer negotiating house price after previous buyer backed out

[Brandon Pierpont]

My wife and I are purchasing our first home.  There was a pending sale on the home in January that fell through.  The house then went back on the market, and was reduced in price by a little under $10k.  The house is perfect for us, as it is right across the street from our son's school, so we have not been negotiating as hard as we otherwise might.  The seller also listed that they would repair/replace HVAC issues for a higher purchase price from a buyer.  We offered a few grand over asking, with the contingency they replace the A/C unit.  They accepted the offer, but had an HVAC contractor provide a quote on the entire system and instead agreed to write us a check instead so we can replace the system ourselves.  The seller apparently doesn't want to deal with repairing the house anymore.  It looks like they have owned the house since 1984, but have been renting it out for the past 10 years.  I just received a copy of the previous inspector's report, and there were some plumbing/electrical issues (that supposedly have since been fixed), high moisture in some areas (so we will need to do a mold test), and a roofing issue on the carport, as well as some wood rot and a few other issues.  

My primary question is this - how much negotiating leverage do I have now that I am the second prospective buyer (one buyer has recently fallen through and that is listed publicly)?  How bad is it for a house to have two broken sales processes within a three month timeframe?  My thought is that this is very bad for the seller, so I probably have some considerable leverage to renegotiate if I find that there are still some substantive issues after we do our own home inspection (which I believe there will be, given the seller's reticence to do repairs).  Thoughts?  Has anyone else dealt with a situation similar to this, and if so what happened?