There are at least 500 pages devoted to threats made against Kennedy -- from groups like the KKK, the Minutemen, the National Socialist White People's Party, as well as from individuals angry about Kennedy's stance on Northern Ireland.
In April 1982, for example, the chairman of the Florida Democratic Party reported to the FBI that a person was calling his office repeatedly and claiming that "Senator Kennedy would be killed by a cross-bow if he decides to run for president." The person "also advised that the subject did not threaten Senator Kennedy personally but advised that this will happen if he runs." The caller identified himself as the "chairman of the Yellowstone Liberation Party" and a member of the National Rifle Association. The details are on page 94 here (.pdf).
In a typical example (.pdf) of the Hoover FBI's intense interest in tracking contact with leftists, a Mexico City-based FBI agent sent a memo to Hoover in July 1961 stating that "As bureau is aware president's brother Edward M. Kennedy presently making tour of Latin America accompanied by Dr. John N. Plank." The agent spoke with Plank, a member of the Harvard faculty, and reported that "Kennedy is interested in meeting with 'Leftists' to talk with them and determine why they think as they do."
On his return from that trip, Kennedy left a black notebook on a Pan American plane, which was retrieved by a passenger and then obtained by the FBI. Before returning it to him, a San Francisco-based agent went through it and summarized Kennedy's notes from the trip in a memo to Hoover. See page 5 here (.pdf).
Concerning Mexico, Kennedy wrote, according to the FBI memo, "On Communists -- they pressent little threat to the great mass of Mexicans because their ideology of the country is firmly entrenched in the ideals of the revolution. ... They hate us, one: because we are rich; two: war of 1847; three: occupation of Veracruz."
There are also plenty of unsubstantiated rumors and bogus tips that made it into the FBI file. As the bureau writes in the introduction to the documents:
[I]t contains report of a rumor from an informant suggesting that elements of the Mafia wanted attack the character of Edward and Robert Kennedy and their brother-in-law Peter Lawford by working through associates of Frank Sinatra to compromise them at a New York party. In the convoluted rumor, both Frank Sinatra and Marilyn Monroe were to be involved. The FBI did not consider the rumor solid, and no other mention of it appears in the file, suggesting that the informant did not supply any corroboration to the story.