I think anyone would be hard-pressed to pinpoint when the NFL began its slide down this slippery slope. It certainly didn't start with Michael Vick, though he's where the spotlight is currently trained. It didn't even start with Randy Moss, who, long before Vick's foray into illegal dog-fighting, was arrested for suspicion of assault with a dangerous weapon (his car). If we look back even further, there are instances of arrests and jail time for drug use, spousal abuse, rape, and even attempted murder all incidents that would endanger any normal person's job. But football players aren't normal people. Or, at least, that's what society seems to have come to believe.
If the NFL is full of thugs, it's the fault of the NFL for not giving these men consequences for their actions. There's no emphasis on ethics or morality, but rather the almighty dollar. Immediately after Vick's arrest, the general consensus seemed to be that Joey Harrington would sell fewer tickets than Michael Vick, making the argument a financial one, rather than an ethical one.
The NFL and every team in it is a business, not a warm and fuzzy family. And the point of a business is to make money. However, the problems begin when key figures upon whom the success of the business depends act like idiots and experience no consequences for their idiocy. What is a $250K fine to someone who makes millions of dollars a year? Fining a player for their behavior isn't a solution, and as long as the player makes the team money, the organization itself can't be depended upon to solve the problem.
While there are players in the NFL who are law-abiding people, the attention (and misplaced adoration) is going to these thugs who, through their actions, make it clear that they have no respect for the law or for the organization that signs their paychecks. They behave as if their job is guaranteed, and as long as they bring in the crowds or as long as their number sells jerseys, they will continue to be employed. The focus is on money and how to make more of it, and somewhere along the line, integrity became something for other people to worry about.
Is it possible for the NFL to redeem itself? Yes, I think so. But it's highly unlikely that the industry will be willing to make the necessary changes to repair its tarnished image.