Is there any problem with whistling in general or to a tune, and is there any difference between whistling during the week or on Shabbos?
Answer:
In general there is no problem in doing so, though some say that it is not 'respectable' practice. Concerning Shabbos, Rema (Orach Chaim 338:1) writes that it is permitted, and Aruch Hashulchan (7-8) adds that it is permitted even when a person whistles by means of placing finger(s) in his mouth. This final point is disputed by Mishnah Halachos (vol. 4, no. 55).