I just found that while the program in general can use a relative large Epsilon (e.g. 1e-5), triangle intersection benefits from a smaller value, say 1e-9 or less. With models that have many small triangles a large Epsilon may cause false misses and lead to visual artifacts.
The model below (100,000 triangles, here rendered in 76 seconds at 64 samples per pixel) improved noticeably with the smaller Epsilon.
Good tip re: triangles. I suspect it has to do with the size of the triangles relative to your chosen epsilon value. Perhaps a rule of thumb is to make sure your epsilon is significantly smaller than your smallest triangle?
I need more tests on the triangles but for so far I could see no difference at 1e-9 or smaller. I also checked explicitly for zero and everything seemed to work, though I feel safer with the Epsilon thing :-P