A screen and recoat MAY take care of the bubbles and the "trash" which I'm guessing are dust particles. Sounds like they didn't vacuum between each coat and/or had windows open.
Screen & recoat will not take care of the cupping. A full sanding will, but all of this comes down to the cause of issue and whether it's been fixed.
The question above the AC is a good one. Note that the temps/humidity should be regulated during acclimation, install, sanding and at least 30 days after last coat of poly.
Also, be sure to wait at least 4 full days from last coat of poly before moving in.
You may find these 2 articles helpful:
http://theflooringgirl.com/blog/hardwoo ... -mean.htmlhttp://theflooringgirl.com/blog/refinis ... -take.htmlDebbie
The Flooring Girl