R' Moshe Sherer brings an interesting explanation from the Chafetz Chaim: The reason for the Torah's double expression of my Shabbos's in ויקרא יט:ג - ואת שבתותי תשמורו is to teach us that our Shabbos observance is incomplete so long as there are others around us who are not Shabbos observant.
שבתותי teaches us that to properly observe שבת. I need to observe my own and do my utmost to ensure that others are keeping theirs. בשתי עינים p48 and http://www.hebrewbooks.org/pagefeed/hebrewbooks_org_50144_6.pdf
I have not managed to find this explanation in any of the Chafetz Chaim's writings (though have come across a different explanations in Shem Olam Chap. 4).