...despite nasty weather. (Para. 3)
Meaning: even with terrible weather; although the weather was very bad. Notice that no "of" is used after "despite". Look at the following sentences:
I went out despite (or in spite of) the rain. 虽然下着雨, 我还是出了门。
Despite (or In spite of) mistakes and weaknesses, it is a good composition. 尽管有错误和不足, 这还是一篇好作文。