restaurant open on shabbat

Question

I tried browsing for a while but couldn't find if this had been addressed before, so if it has, please repeat yourself; What halachic issues, if any, could arise from a vegetarian (with some dairy, clearly marked on the menu, no cheese problems) restaurant, which has hashgacha from a rabbi with whom I am unfamiliar, which is owned by non-Jews and open on shabbat? What in general are the issues with a restaurant which only uses definitely kosher ingrdients but is open on shabbat? Thank you, T