These events are definitely less than desirable. I would hire a home inspector to inspect the work every week or two in order to make sure everything is done correctly. There are many, many things that could be done incorrectly that won't show up for a few years, after the warantee is up. A few hundred dollars for a retainer on an inspector may save you thousands later.
It is a little difficult to fully understand exactly what transpired with your piers and foundation etc.. I am suprised that the piers weren't failed prior to framing. Where I live there is an excavation inspection, a footing inspection, a foundation inspection, etc., etc.. and I don't think it would be possible to start framing with a bad foundation. I am assuming that the inspector passed the footings that they are using. The construction materials are probably ok. Assuming that it was just framing stuff and not trim that was left exposed. The only thing that I can think of that should be checked is the edges of the tounge and groove plywood (or osb) subfloor. If the edges are significantly swelled then this can create ridges at their joints. Check the subfloor with a straight-edge or 4' level to make sure that the joints aren't significantly raised once they get the subfloor plywood down. If they are then they need to belt sand them down flush.