His accomplishments throughout his career include qualifying for 11 Chess Olympiads, with his first one in 1966. He played for Czechoslovakia through 1990, and Slovakia from 1992 henceforth.
In the European Team Chess Championships, Plachetka played for Czechoslovakia in 1973, 1983, and 1989. In terms of individual results, in 1972, he was the Czechoslovakian Chess Championship's co-winner. He also won the Slovan Tournament in Bratislava in 1973, and the Rubinstein Memorial tournament in 1974.
From the mid-1970s through mid-1980s, he competed in five Interzonal tournaments. Noteworthy achievements include semifinals in Riga in 1979 and in Las Palmas in 1982. Plachetka also played in nine Zonal tournaments throughout his career.
In terms of chess journalism, Plachetka has been the chief-editor of a highly-regarded Slovak chess magazine called "Šachové listy" for decades.