I posted an answer to this a while back, in a general discussion of the JFK conspiracy theories (after the release of more official records), and I'll paste it here. The best book on the subject is Vincent Bugliosi's Reclaiming History . It deals exhaustively with all the alternative theories.

Bugliosi devotes a chapter to Jack Ruby and the Mafia, as well as a chapter on Organized Crime. He notes many problems with this[Mafia involvement]. Some of the critical ones:

1)It implies that Oswald was paid by the Mafia to kill JFK. But Oswald was the last person anyone would hire to carry out such an important job. He was clueless, erratic, unreliable, excitable...he might have screwed up the best laid plans. (Allen Dulles, on the Warren Commission, had run many missions in his lifetime and immediately pointed this out).

2)The timing. Ruby had to be nearby, the moment when Oswald was being moved. They [ the Warren Commission] investigated Jack Ruby's movements during that day and it was impossible that he had planned it: he had a window of opportunity of perhaps a minute, to be there when the police car arrived to take Oswald away. Yet he had previously been in the Western Union office, standing in line behind one customer, getting a money order ( the clerk said he was in no hurry, left in no hurry) and was 454 ft. from the scene. No one planning such a thing would have cut it that close. Even if the entire Dallas Police Dept had decided to have him kill Oswald and had told him, he would have been standing there much earlier. As Norman Mailer said, why was Ruby standing in line in the Western Union office for his turn to send $25 to a stripper while time floated away and Oswald might be moved at any moment?

3)Ruby shot Oswald in the stomach, not in the head, meaning Oswald would possibly survive. Ruby did it right in front of law enforcement, who could then apprehend him and perhaps get him to talk about who put him up to it. What powerful criminal organization would do this?

4)Why would the mafia assume that JFK's death would end government investigations of them? RFK was still alive, and motivated, and there was no reason to suppose Johnson wouldn't let him continue.

There's much more than these few points. Bugliosi's book is written in a sometimes annoying , prosecutorial style, but it is worth reading. Generally, it points up a common thread in all of the alternate theories: they find the tiniest inconsistencies in the Warren investigations [of Oswald] and call them highly suspicious, but ignore the huge insurmountable problems with their own alternative scenarios.