The two states where there was significant evidence of voter fraud were Illinois and Texas.
Despite putting a popular Texan on the ticket (LBJ), Kennedy was still very unpopular with rank and file WASP voters in Texas, and lost the non-hispanic white vote in Texas by a slight margin. In order to put him over the top in Texas, the local Democrats reported large numbers of JFK votes in Hispanic regions of the state, and many of these "JFK voters" were likely illegally cast votes -- either they weren't registered, ineligible vote because they were non-citizens, too young to vote, etc. Kennedy winning the Hispanic regions by decisive margins and having big turnout there put him over the top. There was no question many of those RAT voters were illegal aliens. Had those votes been investigated and illegally cast ballots been discarded, there's little question Nixon would have carried Texas.
In Illinois, the vote fraud in Chicago with the Daley machine reporting in the Crook County totals after the state's other 101 counties had reported their numbers has already been discussed.
A third factor that may have resulted in Kennedy losing the popular vote and electoral vote is that a number of deep southern states in the southeast didn't actually vote "for" Kennedy. A lot of the southern RATs couldn't stomach a Massachusetts elite as their nominee, so they voted for "unpledged Democrat electors" to carry their state, not JFK himself. Therefore, although JFK lead by a slight margin in the "popular vote" nationwide and a decent margin in electoral totals nationwide, it was only because the "unpledged Democrat electors" had their arms twisted and were turned into JFK votes when the electoral college met. If they had been following the wishes of "the people" who voted in that state, they would have awarded the state's votes to an alternate RAT, probably a Dixiecrat, so you'd see numbers like 1948 with another RAT gets a couple dozen electoral votes. Without that chunk of the RAT vote, you could make a good case Nixon would have lead Kennedy in the popular vote.
http://www.adversity.net/florida/Frame_Fla_Stories/Kennedy_Daley_1960.htm
There were 68 million votes cast in the 1960 election. The margin between the Republicans and the Democrats (Nixon and Kennedy) was a trifling 113,000 (less than 2/10 of one percent!) in favor of Kennedy.
A subsequent investigation of vote fraud in Illinois and Texas revealed the following:
Fannin County, Texas had only 4,895 registered voters. BUT 6,138 votes were cast, 75% of which went to Kennedy.
Angelina County, Texas: In one precinct, only 86 people voted yet the final tally was 147 for Kennedy, 24 for Nixon.
But Texas refused to conduct a recount. The Texas Election Board consisted entirely of Democrats, and the Board certified John Kennedy the winner in Texas.
(Whoops forgot to reply this thread)
I was gonna say most of the close Kennedy states besides IL (open secret it was stolen at the time, nowadays they don’t bother to deny it they just say “Republicans stole votes downstate”) and TX (40K+ margin but teeming with irregularities and rats had total control of the counting) were suspect. Particularly Missouri, (still home to frequent paper thin rat wins) New Jersey and New Mexico.
Not to mention they needlessless stole Hawaii via recount after Nixon conceded.
And the Dixiecrat situation you mentioned, that was in Alabama. So even in the official count Nixon may have been the legitimate popular vote winner.