I have read about a couple of corrosion concerns with stainless steel surface finish. I don't have any direct experience with differing rates of corrosion, but below are some considerations:
The smoother the finishes are less likely to collect dirt and water on the surface. Each of these will help to increase the local rate of corrosion. Some smooth (mirror-like) finishes are even considered "self cleaning" from an architectural stand point.
This is related to #1 above. When finishes have a defined brush pattern, the brush lines should be oriented vertically. This helps to allow water and dirt to flow downward instead of collecting.
Fasteners and Hinges
Fasteners and hinges will have some of the same issues. Any location where water and dirt will collect will likely show increased corrosion.
Another consideration is galvanic corrosion. This is increased corrosion that occurs when two different types of metals are in contact. This can be common if hinges and fasters aren't also made of stainless steel.
A manufacturer's website that has more information about the different finishes can be found here.
In aggressive environments, such as in the nuclear or offshore industries, a correctly polished stainless steel surface has a better resistance to corrosion than a surface that is roughly or badly polished. A smooth surface is less susceptible to an accumulation of deposits and stainless, which often become focal points for localised corrosion.