I think most of Gruden's detractors question his talent evaluation skills (or lack of) and question whether or not he truly has "the juice" (one of Gru's favorite words) to inspire players to play up to their potential. Others more will say that he's not nearly the offensive genius or great teacher that his brother is.
Personally, I think Gruden is better than most of the guys holding down an HC job in the league right now. He is also very likely to command a top tier salary with expanded powers, if he were to leave the booth next season. With his sons now headed off to college, I'm sure he's getting that itch to get back in the game. My money is on him replacing Reid in Philly. (Note: Deuce Gruden, Jon's son, attends college in Easton, PA.)