What significance or symbolism, if any, is there if a person sees a torah scroll fall to the floor in a dream?
See Magen Avraham OHC 288/6 quotes the Sefer Magid Mesharim (Vayakhel) which states that the Beis Yosef was told by the "Maggid" that he was correct in ruling that only 3 dreams allowed fasting on Shabbos, [one being one who dreams that a Sefer Torah was burned], but one who dreams of a Sefer Torah falling on Shabbos should not fast then.
Rabbi Tzvi Hirsh Berliner in his Sefer Kol Hatorah deduces from this that during the week one must fast when dreaming about a Sefer Torah falling. [http://beta.hebrewbooks.org/pdfpager.aspx?req=48972&pgnum=8]
Rav Zivotofsky understands the Mishna Berura (288:16) that one does not need to fast for seeing a sefer torah fall in one's dream.
See here for the full article:
Although there is a popular notion to fast even on Shabbat for dreadful dreams, including a dream in which one saw a Torah or tefillin burnt (Shulchan Aruch, OC 288:5), that is not the case for seeing them fall in a dream
Seemingly, such a dream would not necessarily be something to worry about. The Gemara Berachos (57a) mentions our dreams don't portend much meaning when we thought about the idea during the day. Worrying about someone accidentally mishandling the Torah from the Aron or Hagbah is an occurrence which some people occasionally think about.