Am I mistaken in believing that "kurtka" can mean "coat" just as easily as "jacket?" I was marked incorrect for this, and would like to know if this is formally wrong.
Indeed. "Kurtka" and "płaszcz" are totally different things, the first being simply a jacket, second - a coat.
Well, what I usually think of as a jacket is "marynarka" or "żakiet" (for women). Athough certainly different from "płaszcz", and often called a jacket, "kurtka" can sometimes also be referred to as a coat (especially the outdoor type). The PWN/Oxford "Wielki" lists both.
"płaszcz" as in overcoat or raincoat is "coat", yes, but there are other types of coat, some of which (like the one I wear) would be translated as "kurtka". Languages don't always have a 1:1 exact match in meaning.
Yes, it can mean a short coat. As for jacket, it means the kind of jacket you put on to go out in, not as in suit jacket, sports jacket, etc, which is "marynarka" for men, or "żakiet" for women.