All Greek to Me (or is it Latin?)

One of the criticisms of"The Passion" (haven't seen it yet) is that the Roman soldiers and Pilate should be speaking Greek to each other, not Latin. Some of these critics have said that Greek was the language of the" common people" in the Empire.

I have a question that perhaps an expert can answer. If Greek was the language of the common people (including presumably the Roman army) why do so many European peoples have Latin-based languages including Romanian, Italian, Spanish, etc.? What were the common people in those areas speaking at the time? If it was Latin, then it would seem to make perfect sense that at least some of the Romans (many of them originally from these areas) stationed in Judea would have been speaking it to each other.