A few obvious ones:
110.3(A)ox is not listed for installation method used to attach to grid ceiling member.
Round ceiling fixture adapter plate is not listed for use with a square box.
110.3(B) installation per listing; box has been modified, listing is voided, box must be replaced.
Round ceiling fixture adapter plate is not installed in accord with listing by attachment to a round box, attachment to ceiling grid must be removed.
300.11(A) Cables and raceways are not allowed to be supported by ceiling grids. Since the box is not secured to grid, the cable is effectively supported by the grid.
Got tired of looking at this mess. If I found it during an installation inspections, I would turn the electrician in to the license board and write one correction; all electrical system installation to be inspected and corrected by a competent licensed electrician.