The Reliability of Pre-modern Sources

I recently saw a link to an article which described an experiment proving that the "legendary" death ray of Archimedes could have been real. The account prompted me to reflect on the deep skepticism with which most moderns view ancient and medieval accounts of all sorts.

I suppose it is post-Renaissance arrogance and disdain for the past which leads to the dismissal of stories of advanced technologies and supernatural events. We [the MLA program] reject modernism as well as post-modernism, or say we do, but I wonder how many modern prejudices are still ingrained in us. Would I have countenanced the possibility of Archimedes's death ray in the absence of this new "scientific" account? I don't know.

What degree of faith or skepticism should we have when we approach documents produced in a different age, when the standards to which we are accustomed did not apply?