A little late to the party. I am on the fence about Jackson. Yes, he took money and the idealist in me says that if he knew about it, took the money and did nothing to stop it, it was aan assault on the integrity of the game that should deny him access to the Hall of Fame. But the other half of it is that he played in an era when things were so different than they are now. Comiskey was such a prick, and so cheap with his players, and while those guys earned nice salaries compared to the typical person on the street, they were not getting wealthy from baseball. So taking the money was probably less a case of "blind, arrogant greed," than him feeling he was just getting what he was owed from Comiskey, who dicked his players every opportunity he got. I could be swayed either way about Jackson. If a player today, earning $2 million a year, threw World Series games for a payoff, it would make my blood boil in a way that Shoeless Joe Jackson doesn't.
Knowing how I feel about cheating and integrity, this may surprise some, but I absolutely think Pete Rose belongs in the Hall of Fame. His gambling does not change when he did on the field as a player. If there was any evidence that he ever did anything to throw a baseball game, it would be one thing. But there isn't.
Baseball should have a hard line when it comes to anyone associated with the game doing any sort of gambling on the game. Keep Rose away from being honored at official baseball ceremonies. Ban him from the game. Make it clear to everyone that he dipped his toe in a pool that he knew was off limits. But that still doesn't change what he did as a player, and as a player, he is Hall of Fame worthy.