i had wireframes showing over my render. (i dont know if that's the same thing the OP had, with 'edges of polygons showing,' but it sure looked the same.)  what i did that fixed it...

 

i had the main light that was depth-map shadowing, and i changed it to ray trace.  then i turned on AO for it.  the default shadow min bias was 0.0 (which apparently doesn't work?)  changing it to 0.1 made it render fine.

 

why on earth anything would make the wireframe render is beyond me.

btw, all the right side checkboxes in the render prefs were UNchecked, including smooth and backface stuff.  (both before and after the fix.)