I don't know if I should remain concerned about the tub. As mentioned here ( http://www.houserepairtalk.com/f45/final-thoughts-renovation-14289/
), there was a draft when, after the installation, the grout around the tub edge cracked - joecaption was right to note insulation/drywall was missing. I think some mortar was put under the tub since, after complaints to the contractor thanks to my wife's persistence.
For the cut that he made to the edge of the tub, we had the contractor sign a separate warranty for I think 5 years.