Frank Sinatra and his ''Rat Pack'' -- Dean, Sammy, Joey, and Peter -- held court at its Carnival Supper Club. And there were the hundreds of thousands of tourists, who strolled through the Sheraton Bal Harbour hotel's majestic and mosaic lobby during its half-century existence. Sunday morning, with a staccato series of booms, it all became part of the past. The hotel, which opened to the public in 1956 as the Americana, came tumbling down.