"Mafia ties" to the Kennedys have been rumored for decades, even before the JFK assassination. They're based on two thin threads of circumstance:
1. Joe Kennedy was a major importer of Scotch whiskey during Prohibition--ergo, he must have had Mafia ties to do so. Nope. The Mafia (that is, organized crime Mafia families of the Twenties) was NOT a major player in Prohibition-era rumrunning. Jewish and Irish gangs dominated most of the Prohibition-era booze business, except in Chicago, where the Capone mob (which was NOT a Mafia family) was the big player. Joe Kennedy may have had some ancillary business with organized crime-connected people who bought or shipped his booze, but that doesn't constitute an intimate connection.
2. In a hip-bone-connected-to-thigh-bone story, JFK was rumored to have a connection to Sam Giancana, Chicago Mafia boss. According to this tale, Frank Sinatra, who was briefly a pal of JFK's, introduced him to Judith Campbell Exner, who had been Giancana's mistress. Later, supposedly, JFK or his father asked Sinatra to ask Giancana to turn out the labor vote for JFK in the 1960 election. It is a fact that Exner was one of JFK's (many) mistresses, but he dropped her (and Sinatra) like the proverbial hot potato when FBI boss J. Edgar Hoover revealed that he knew about the liason and her connection to Giancana. And it's unlikely that JFK, his father or Sinatra asked Giancana for any help in 1960, since Chicago's all-powerful mayor, Dick Daley, had promised his ally JFK that he'd delive the state of Illinois on a silver platter. Nor would Giancana have been willing to help JFK: only the year before, JFK chaired a Senate committee hearing on labor racketeering at which brother Bobby (the committee's counsel) called Giancana as a witness and humiliated him--likening him to a "little girl."
For the record: I agree with Apple about JFK not being a great (or even near-great) President. Martyrdom has greatly exaggerated his status.