"Who is responsible for leaving the window open?"
Translation:¿Quién es responsable de dejar la ventana abierta?
Generally for means por o para, but it can be translated for other prepositions like hacia, aunque, a lo largo, or de. You could use "por" instead and it would be understood, but the natural preposition here is "de".
Ser resposable de (Be responsible for, in charge of, accountable for)
"Dejar", in Spanish, can mean either "leave", "let", "lend" ..http://www.wordreference.com/es/en/translation.asp?spen=dejar ,; "seguir" can mean "go on", "continue", "follow".. http://www.wordreference.com/es/en/translation.asp?spen=seguir. It depends on the sentence.
Would "Quien esta responsable por dejando abierta la ventana?" also have this meaning? It seems like this one would mean someone has the responsibility of making sure the window is left open, and duolingo's would mean that someone did leave the window open, and we want to know who did it.