What safety issues led the FAA to ban Constellation flights into/out of the U.S.?
Individual airlines, or even all of the airlines from entire countries, are sometimes banned for safety reasons. It was the Dominican airlines, not the aircraft, that were banned by the FAA.

It is just coincidence that many of these un-safe airlines flew Lockheed Constellations. They were banned from flying ANY aircraft into the USA. 

The Wikipedia article talks about the end of Constellations used in commercial airline service, but it was the grounding of the airlines that caused the end, not the grounding of any particular aircraft. 

Here is a link to a NY Times article describing a ban of all airlines from nine different countries. 

Sept 3rd 1994 NY Times article


  The Federal Aviation Administration has barred airlines from nine nations from flying to the United States because of poor safety procedures.
  
  The unusual action, announced today, is a response to safety questions
  from consumer groups. Officials say they hope the economic fallout of
  the ban will encourage the airlines to follow safety guidelines.
  
  The aviation agency surveyed safety procedures in 30 of the 93
  countries that have commercial flights to the United States. The
  agency sought to determine if the aviation authorities in each country
  were meeting the safety requirements of the International Civil
  Aviation Organization, a United Nations agency. Its rules are less
  strict than those of the Federal Aviation Administration.
  
  The aviation agency did not reveal details about the safety
  deficiencies that had prompted it to ban the nine airlines.
  
  The banned airlines are from Belize, the Dominican Republic, Gambia,
  Ghana, Honduras, Nicaragua, Paraguay, Uruguay and Zaire. Four other
  countries were allowed to continue flying into the United States, but
  under increased supervison by the aviation agency. They are Bolivia,
  El Salvador, Guatemala and the Netherlands Antilles.