Forget the Mafia and the CIA.
The often quoted statement that JFK wanted to "splinter the CIA into a thousand pieces" was made two and a half years before the assassination. In the ensuing period,not only did JFK not make any moves to disband the Agency,but he also passed the largest CIA appropriations package in the history of the CIA.
So if I have this right,the CIA figures "Hey this guy gave us more money than any President in the history of the US,so let's kill him because of something we think he might have said years ago". Yea,we'll show him".
On the subject of the Mafia,in the course of the last fifty years,not one credible piece of evidence has surfaced tying anyone but Oswald to the shooting.I know we have the ramblings of megalomaniacs claiming that they were in on it,and second and third hand "recollections" of discussions tying any one of a dozen mob guys to the hit,but if there were anything to it,we would have some hard evidence.
If you look at the thousands (maybe tens of thousands) of wiretaps that OC investigators have amassed over the last fifty years,along with all of the Mob guys that have caught serious sentences over the same period,and would have a major bargaining chip,not one,repeat,not one piece of evidence,or credible snitch testimony has surfaced.
The problem with the majority of conspiracy theories is that people hear or read something and stop there. If people would just follow a simple principle of "Don't rePEAT,reSEARCH, a lot of this stuff would go away.