Can a 1x4 jack stud be used instead of a 2x4?
Have him re-frame it, as it almost certainly won't pass inspection.  Not sure what the code specifies in you area, but the International Residential Code is really specific as to the requirements:


  R603.7 Jack and king studs.
  
  The number of jack and king studs installed on each side of a header
  shall comply with Table R603.7(1). King, jack and cripple studs shall
  be of the same dimension and thickness as the adjacent wall studs.


Emphasis is mine.