He was mostly cast in roles of cold, cynical and detached middle-aged gentlemen, though at times he also portrayed lovers and even comedic characters.[1] He also appeared in numerous films, including Podhale w ogniu, Andrzej Munk's Heroism, Knights of the Teutonic Order, Ogniomistrz Kaleń and Stawka większa niż życie TV series, as well as numerous films shot for the Television Theatre, that is theatrical plays recorded for the Polish Television.[1]
Kostecki retired in January 1973.[1] He died 18 August 1980 in Warsaw and was buried at Wólka Węglowa cemetery of Warsaw.[1]
(in Polish) Barbara Berger (1994). Zbigniew Wilski (ed.). Słownik biograficzny teatru polskiego [Biographical dictionary of Polish theatre]. Vol. 2: 1900-1980. Warsaw: Polska Akademia Nauk, Wydaw. Naukowe PWN. p. 862. ISBN978-83-01-11260-8. PB 1994/1883., as cited in: "Józef Kostecki". e-teatr.pl - polski portal teatralny. Instytut Teatralny im. Zbigniewa Raszewskiego. 2010. Retrieved 2015-01-09.