"I look through the colorful window in the bathroom."
Translation:Jeg kigger gennem det farverige vindue i badeværelset.
Pure conjecture here (partially to motivate a correct answer to swoop in) but as I recall all the things that were "på badeværelset" or "på slottet" were humans/people. In this case it is a feature of the room, an object, so maybe that is the qualifying difference that means in this case we use "i".
edit: I found the translation in Determiners to "He has few books in his room" as "Han har få bøger på sit værelse." This seems to contradict what I suggested. So, I don't know!
Both are correct. it depends from where you are standing and looking, if you look from the living room or from the bathroom.
in the sentence above it is impossible to guess, so both are right. The person who wrote the sentence obviously knows the layout he describes, then I suppose he used "i" intentionally and it is not a mistake